signal processing in acoustics: science or science … · lar application has led to many advances...

encompass all of the techniques used toextract the useful information from data.Such techniques as image processing,tomography, array processing, spectralprocessing, model-based processing, etc.are implied by this terminology) forms

the basic nucleus of many acoustical applications. It is a spe-cialty area that many acousticians apply in their daily techni-cal regimen with great success such as the simplicity inFourier analysis of resonance data or in the complexity ofanalyzing the time-frequency response of dolphin sounds.Acoustical applications abound with unique signal process-ing approaches offering solutions to the underlying problem.For instance, the localization of a target in the hostile under-water ocean acoustic environment not only challenges theacoustician, but also taxes the core of signal processing basicsthereby requiring that more sophistication and a prioriknowledge be incorporated into the processor. This particu-lar application has led to many advances both in underwatersignal processing as well as in the development of a wide vari-ety of so-called model-based or physics-based processors. Aprime example of this technology is the advent of the model-based matched-field processor7-9 that has led not only to asolution of the target localization problem, but also to manyapplications in other acoustical areas such as nondestructiveevaluation and biomedical imaging. So the conclusion is thesame, signal processing is a necessary ingredient as a workingtool that must be mastered by the acoustician to extract theuseful information from uncertain measurements.

AcousticsLet us look at acoustical signal processing from a slight-

ly different perspective. Acoustical data can be used toextract useful information about signal sources, the sur-rounding environment and background noise much the sameas any other modality (e.g., electromagnetics: radio frequen-cy (RF), infrared (IR), optics, etc.). The information is clear-ly different but can also be used effectively. The uniquenessafforded is determined by how the acoustic signals propagatewithin the particular environment. The information availableor carried by the acoustic signal (wave) depends heavily onthe source characteristics and the environment supportingthe propagation in which the wave interacts or causes thesesignals to bounce, bend and spread in a multitude of direc-tions distorting both their shape and arrival times at sensorlocations. Localization (incoherent) of the source is per-formed by estimating the arrival times (time delays) andusing geometric relations (triangularization). The sourcecharacteristics also determine the underlying acoustical

SIGNAL PROCESSING IN ACOUSTICS:SCIENCE OR SCIENCE FICTION?

Signal processing in acoustics isbased on one fundamental con-cept—extracting critical informa-

tion from noisy, uncertain measurementdata.1-5 Acoustical processing problemscan lead to some complex and intricateparadigms to perform this extraction especially from noisy,sometimes inadequate, measurements. Whether the dataare created using a seismic geophone sensor from a moni-toring network or an array of hydrophone transducerslocated on the hull of an ocean-going vessel, the basic pro-cessing problem remains the same—extract the usefulinformation. Techniques in signal processing (e.g., filtering,Fourier transforms, time-frequency and wavelet trans-forms) are effective; however, as the underlying acousticalprocess generating the measurements becomes more com-plex, the resulting processor may require more and moreinformation about the process phenomenology to extractthe desired information. The challenge is to formulate ameaningful strategy that is aimed at performing the pro-cessing required, even in the face of these high uncertain-ties. This strategy can be as simple as a transformation ofthe measured data to another domain for analysis or ascomplex as embedding a full-scale propagation model intothe processor.5-7 For example, think of trying to extract a setof resonances (damped sinusoids) from accelerometer timeseries. It is nearly impossible to calculate zero-crossingsfrom the time series but it is a simple matter to transformthe data to the spectral domain using the Fourier transformand then applying the property that sinusoids are impul-sive-like in Fourier space facilitating their extractionthrough peak detection. Finding a sinusoidal source propa-gating in the ocean is another matter that is quite complexdue to the attenuation and dispersion characteristics of thisharsh environment. Here, a complex propagation modelmust be developed and applied to “unravel” the highly dis-torted data to reveal the source—a simple Fourier trans-form will not work. The aims of both approaches are thesame—to extract the desired information and reject theextraneous, and therefore, develop a signal processingscheme to achieve this goal. In this article, we briefly dis-cuss this underlying signal processing philosophy from a“bottoms-up” perspective enabling the problem to dictatethe solution rather than vise-versa. Once accomplished, weask ourselves the final and telling question, “Did it work orare we kidding ourselves?” Are the results science or arethey science fiction?

More specifically, signal processing (Note that through-out this article we will use the term “signal processing” to

“…to extract the desired

information and reject the

extraneous…”

James V. CandyLawrence Livermore National Laboratory and

University of California, Santa Barbara Livermore, California 94551

6 Acoustics Today, July 2008

operational frequency band and therefore the sensors used tomeasure the propagated data with wavelengths inversely pro-portional to the source frequency. Clearly, compared to RFtransmissions, acoustic waves propagate at long wavelengthsand are affected by materials much differently.1-4 Scattering ofwaves is determined by the object size at a wavelength or less.The point is that the advantage or disadvantage of acousticalwaves over other modalities is determined by the acousticalproperties of the source as well as the materials composingthe propagation medium or environment. For instance, theaudible acoustic range is the frequency band from 20 Hz to20 kHz and is measured by microphone sensors, while seis-mic signals reside in the 0 to 10 Hz band measured by net-works of geophones. Inaudible ultrasonic signals are typical-ly in the 20 kHz to 20 MHz regime measured by piezoelectriccrystal sensors.1,3,4

Acoustics can be used to perform the usual tasks ofdetection, classification and localization much the same asRF with sonar replacing radar in the active problem. Forinstance, acoustic sources can be localized by triangulariza-tion techniques much like finding the epicenter of an earth-quake by a worldwide network of seismometers using theirknown location and the arrival times of the seismic event.Because of the large wavelengths in acoustic signals, arrayscan be designed for coherent (phase) processing, that is, anarray of acoustic sensors can be used to localize an acousticsource and passively scan an environment through beamsteering while using beamforming techniques to search forsources. The human ear is a perfect example of passive(coherent) source localization in the audible range. In morecomplex environments, physics (model) based techniquescan be used to enhance further the measured signal and per-form the localization.5-7

The processing of acoustic data is necessary toextract the desired information from the noisy measure-ments. For example, if a voice recording was available, thenthe microphone data could be processed to separate the voicesignature from the environmental background and noisethereby decomposing the acoustic information of each.Kennedy assassination data was thoroughly analyzed frommicrophone data acquired from available audio andvideo/audio recordings. The number and location of shotsfired were extracted from the recordings.2 The frequencycharacteristics of the sounds were analyzed even further toextract information about the environment (time-frequencyestimation). Active acoustics (sonar) is typical in many appli-cations ranging from the underwater tracking of a movingtarget, to locating tumors in tissue for biomedical applica-tions, to imaging materials using an acoustic microscope.Vibrational acoustic signals provide critical informationabout structures and their condition in structural integritystudies. Thus, acoustical data much like RF or radar datauniquely provides information about the source, backgroundenvironment, and noise that can be processed to extract use-ful information depending on the source characteristics andthe supporting propagation medium as well as objects popu-lating that particular environment (e.g., urban environmentwith buildings).

Signal processing approachSignal processing relies on any a priori knowledge of the

phenomenology generating the underlying measurements.Characterizing this phenomenology and propagation physicsalong with the accompanying measurement instrumentationand noise are the preliminaries that all acousticians musttackle to solve such a processing problem. In many cases thisis much easier said than done. The first step is to determinewhat the desired information is and typically this is not thetask of the signal processor, but that of the acoustician per-forming the study. In our case, we assume that the investiga-tion is to extract information stemming from acoustic signalseither emanating from a source whether it be an autonomousunmanned vehicle (AUV) passively operating in the deepocean or a vibrating structure responding to ground motion.Acoustic applications can be very complex especially in thecase of ultrasound propagating through complex media suchas tissue in biomedical applications or through heteroge-neous materials of critical parts in nondestructive evaluation(NDE) investigations.1,3,4 In any case the processing usuallyinvolves manipulating the measured data to extract thedesired information, such as, location and tracking of theAUV, to failure detection for the structure, or tumor/flawdetection and localization in both biomedical and NDE.6,7

Another view of the same problem is to decompose itinto a set of steps that capture the strategic essence of the pro-cessing scheme. Inherently, we believe that the more a prioriknowledge about the measurement and its underlying phe-nomenology we can incorporate into the processor, the bet-ter we can expect it to perform—as long as the informationthat is included is correct. One strategy, called the “model-based approach,” provides the essence of model-based signalprocessing.6,7 Some believe that all of the signal processingschemes can be cast into this generic framework. Simply, themodel-based approach is “incorporating mathematical mod-els of both physical phenomenology and the measurementprocess (including noise) into the processor to extract thedesired information.” This approach provides a mechanismto incorporate knowledge of the underlying physics ordynamics in the form of mathematical propagation modelsalong with measurement system models and accompanyinguncertainties such as instrumentation noise or ambient noiseas well as model uncertainties directly into the resultingprocessor. In this way the model-based processor enables theinterpretation of results directly in terms of the problemphysics. The model-based processor is really an acousticmodeler’s tool enabling the incorporation of any a prioriinformation about the particular application problem toextract the desired information. As depicted in Fig. 1, thefidelity of the incorporated model determines the complexi-ty of the processor. These models can range from simpleimplied non-physical representations of the measurementdata such as the Fourier or wavelet transforms to parametricblack-box models used for data prediction, to lumped math-ematical physical representations characterized by ordinarydifferential equations, and to full physical partial differentialequation models capturing the critical details of the acousticwave propagation in a complex medium. The dominating

Signal Processing in Acoustics 7

oscillation frequency). Ourfirst “simple” approach to ana-lyze the measurement datawould be to take its Fouriertransform and investigate thevarious frequency bands forresonant peaks. The result isshown in Fig. 2b, where webasically observe a noisy spec-trum and a set of potential res-onances—but nothing reallyconclusive. Next we apply abroadband power spectral esti-mator with the resulting spec-trum shown in Fig. 2c. Here wenote that the resonances haveclearly been enhanced andappear in well-defined bandswhile the noise is attenuated bythe processor, but there stillremains a significant amountof uncertainty in the spectrumdue to all of the resulting spec-

tral peaks. Upon seeing these resonances in the power spec-trum, we might proceed next to a gray-box model to enhancethe resonances even further by using our a priori knowledgethat there is essentially one dominant resonance we seek. Theresults of applying this processor are shown in Fig. 2d.


factor of which model is the most appropriate is usuallydetermined by how severe the measurements are contami-nated with noise and the underlying uncertainties encom-passing the philosophy of “letting the problem dictate theapproach.” If the signal-to-noise ratio (SNR) of the measure-ments is high, then simple non-physical techniques can be used toextract the desired information.This approach of selecting theappropriate model is depicted in thesignal processing staircase of Fig. 1where we note that as we progress upthe “modeling” steps to increase theSNR, the complexity of the modelincreases to achieve the desiredresults. In the subsequent sections ofthis article, we will use the model-based framework to explain the var-ious classes of acoustical signal pro-cessing problems and attempt toshow—even at a simple level—howthese schemes can evolve within thisframework. This is our roadmap.5-7

Signal processing stepsWe start with the simple first

step and show how we can progressup the signal processing staircase toanalyze a problem. Suppose we havea noisy acoustical measurement(Fig. 2a) of a single oscillation fre-quency in random noise (SNR = 0dB, i.e., equal values of signal tonoise) and we would like to extractthe desired information (the single

Fig. 1. Signal processing approach: the model-based “staircase.” [Step 1] “Simple” non-parametric implicit models. [Step 2]“Black-box” models (transfer function, autoregressive, moving average, polynomial, etc.). [Step 3] “Gray-box” models (trans-fer function, autoregressive moving average, etc.). [Step 4] “Lumped” physical ordinary differential equation models (state-space, parametric, etc.). [Step 5] “Distributed” physical partial differential equation models (state-space, etc.).

Fig. 2. Simple oscillation example. (a) Noisy oscillation (10.54 Hz) in noise. (b) Raw Fourier spectrum. (c)Nonparametric spectrum (black-box). (d) Parametric spectrum (gray-box). (e) Model-based spectrum (ordinary dif-ferential equation model).


Finally, we use this extracted model to develop an explicitmodel-based processor (MBP) by developing a set of har-monic equations (ODE) for a sinusoid in noise and constructthe MBP based on these relations. The results are shown inFig. 2e. So we see that once we have defined the acousticalproblem, and assessed the a priori information including theunderlying phenomenology, then we can proceed up thestaircase and exit any time we are satisfied with the result.This is the “bottoms-up” approach.7

Next we choose to investigate this approach in moredetail by selecting some processing areas with an accompa-nying set of acoustical applications. Here we illustrate notonly the fundamental approach to problem solving, but alsoto observe some of the popular processing paradigms avail-able to the acoustician for analysis and information extrac-tion. Our aim is to define a specific problem that representsa class of problems and then show some of the potential sig-nal processing solutions available, demonstrating themthrough simulation or experiments.

Step 1: Simple spectral estimation techniquesClassical spectral analysis is a very powerful example of

a set of tools that have evolved in signal processing especial-ly in acoustics. Here a raw measurement is “transformed” tothe spectral or Fourier domain for analysis. Modern tech-niques of spectral estimation can be considered both “blackor gray-box” processors and even physics-based processorsdepending on the underlying application.5 We call the black-box/gray-box methods “parametric processors,” since theyemploy a variety of underlying model sets to achieve theirenhancement and improved spectral estimation. Thus, theparametric spectral estimator consists of a processoremployed to estimate the parameters of the underlying

model set and then perform a power spectrum estimate usingthis model.

Modern spectral analysis techniques easily extrapolate tothe space-time domain as long as we assume that the incom-ing wave front is separable in space (array) and time (or fre-quency). In this context, we can consider a measurementarray as a spatial sampler of the arriving wave front. If we fur-ther assume that the temporal portion of the wave is restrict-ed to a narrow frequency band, then we collapse its temporalresponse to a single frequency line (in the Fourier space) thatcan also be considered a parameter. So we see that estimatingthe arrival angle in the case of a planar wave front or thesource location in the case of a spherical wave front can beconsidered a problem of “spatial” spectral estimation and allof the usual modern techniques (with some restrictions)apply to the array signal processing problem as well.5,7

In acoustics, a large set of problems reduce to array pro-cessing or spatial spectral estimation in this context. Suchproblems as ocean acoustic (sonar) signal processing for tar-get direction-of-arrival (DOA) estimation or localization fallinto this category along with ultrasonic NDE and biomedicalprocessing searching for flaws or abnormalities.1-4 Clearly,seismic array processing, of which most of these ideas evolve,is a root application of arrays for epicenter location andvelocity estimation. With this information at hand, let usconsider a simple example of a plane wave impinging on asensor array to convey these ideas using a concrete example.

Spectral (spatial) estimation for direction-of-arrivalSuppose a 16-element linear array with acoustic sensors

uniformly spaced at 2.5m is impinged upon by a set of planewaves generated from three (3) sources emanating from 20o,40o, and 55o incidence angles. The temporal frequency is

Fig. 3. Modern spectral (spatial) estimation using the maximum entropy method parametric estimator for direction-of-arrival estimation of three plane waves at 20o, 40o,55o arrival angles; (a) Synthesized 16-element array temporal measurements (signal-to-noise = 0 dB) with true source locations; (b) Maximum-entropy-method spatialspectral estimation results with estimated arrivals at 20.4o, 40.0o, 53.6o generated from an ensemble of 256 realizations.

age (pole-zero), state-space, etc.); (2) estimate the modelparameters from the data; and (3) construct the signal esti-mate (e.g., spectrum, impulse response, etc.) from theseparameters.7 Again this can represent the “black-box” step ifthe parameters have no physical interpretation or the “gray-box” step if they do have physical relations.

Parametric signal processing for prosthetic heart valveclassification application

As a parametric processing application, consider theproblem of estimating flaws or cracks in prosthetic heartvalves (see Fig. 4a). By placing microphones on a patient’schest and listening to the sounds radiated by the valve, itscondition can be determined. From the structure of the pros-thetic value and its interacting components, it is possible toisolate the sounds associated with each component and clas-sify potential problems. Since these sounds are essentiallyvibrational resonances, an all-pole (autoregressive) model isselected to perform parametric signal processing and investi-gate the condition of the valve under test through a variety ofstatistical tests. Note how the acoustical problem is dictatingthe processing approach and potential solution. The process-ing is illustrated in Fig. 4. The approach selected in this appli-cation is to construct a classifier to determine in which class(failure or normal) the valve belongs (Fig. 4b). The heart

300 Hz with corresponding propagation speed of 1500m/sec. The sensor data are generated at 0 dB SNR. Theresults of applying a modern parametric estimator (maxi-mum entropy method (MEM))5 developed for harmonic(sinusoidal) waves in noise are shown in Fig. 3, where weobserve the ensemble results of the 16-sensor channel spec-tral estimates. The results demonstrate that the algorithmsare capable of providing reasonable DOA estimates in such anoisy environment.

Steps 2 & 3: Parametric signal processing (black/gray-box approach)

Perhaps even a more reasonable application of modernsignal processing follows directly from the black/gray-box orparametric approach. In this realm of processing the acousti-cian can choose from a set of models that reasonably approx-imate the underlying phenomenology and essentially “fit” themodel to the data through a variety of estimation algorithms.This type of processing evolves from the signal processing lit-erature, from applications in speech (e.g., linear prediction,coding, recognition, etc.),10 and controls called system identi-fication (e.g., adaptive control, noise cancelling, etc.).11 In thisdomain the parametric approach is to: (1) select a represen-tative model set (e.g., transfer function, autoregressive (all-pole), moving average (all-zero), autoregressive moving aver-

Fig. 4. Prosthetic heart valve acoustic analysis and condition detection using parametric signal processing (black/gray-box) techniques: (a) prosthetic heart valve under test;(b) overall processing paradigm to detect and classify condition; (c) parametric (all-pole) model and estimated signal/spectrum; and (d) ensemble spectrum, instantaneousspectrogram (power versus time versus frequency) image, and peak frequency probability distribution or histogram (feature) for condition classification.


valve radiates a sound witheach beat that is measured bythe microphone(s) positionedon the patient’s chest. The noisymeasurement data is enhancedand initially analyzed (Fig. 4c)and then processed further.Here a spectrum and instanta-neous spectrogram are estimat-ed from the model parametersand displayed in Fig. 4d. Thefrequency peaks in the spectro-gram are estimated, and a peakresonant frequency probabilitydistribution histogram is con-structed to provide a featurevector that can be used to per-form the classification deter-mining the valve’s condition.12

Step 4: Model-based processing (lumped physical approach)

Model-based signal pro-cessing7 is the next step in thesignal processing approach. Ithas distinct advantage overother approaches because the processor is developed directlyin the acoustician’s frame-of-reference, that is, in his phenom-enological space. Not only does it require physics-based mod-els of the underlying phenomenology, but it also requiresknowledge of the measurement instrumentation and noiseprocesses to construct a good processor. Here the acousticianis “thinking” directly in terms of the acoustics and not infer-ring results from a variety of analysis tools (e.g., Fourier andwavelet transforms) that are not directly related to the under-lying propagation physics. The model-based approach is sim-ply incorporating mathematical models of the underlying phe-nomenology including measurements and noise into the pro-cessing scheme—this is exactly how the acoustician becomesan integral part of the processing by providing the acousticmodels that are embedded into the model-based processor(MBP). Not only is there direct benefits of thinking in thesame physical coordinates of the acoustic problem, but alsogaining a deeper understanding of the instrumentation per-formance and noise/uncertainty processes that contaminatethe problem. This is the good news. Of course, if the model isinaccurate and does not represent the phenomenology ade-quately, then the results can be erroneous and sometimes verymisleading (science or science fiction?). Fortunately, many ofthese processors provide “self-checking” validation tools suchas residuals (difference between the measurements and modelpredictions) that can be statistically tested for validity and usedby the processor to assure accurate performance.7 With this inmind, we introduce two of the most popular model-basedapproaches in the literature: model-based matched-field pro-cessing8,9 (imaging) and model-based recursive (in-time or in-space or both) processors (e.g., MBP or Kalman filters).7

Model-based matched-field imaging for nondestructiveevaluation

Typical image processing techniques in acoustics consistof pre-processing the raw data to provide enhanced signals asinput to the image formation algorithm as well as post-pro-cessing of the two-dimensional image to enhance, extract,and classify certain features of high interest. In this article, weconcentrate primarily on the same theme that we have usedthroughout, the development of processors that incorporatemore and more a priori information about the acoustics gen-erating the data and its incorporation into a model-basedimaging algorithm.

We saw in the previous example of a plane wave imping-ing on an array, how modern spatial spectral estimators(beamformers) can be used to estimate the wave’s spatial andtemporal spectral features. The model-based approach usesall of the a priori information about the plane wave propaga-tion and noise measurements to extract the parametersdirectly solving the problem. The same idea can be extrapo-lated to the imaging problem. We assume that we have anarray of sensors either physical or synthetically created, andwe have developed a sequence of measurements resulting byexciting the medium under investigation. For instance, it canbe an active sonar system in the ocean or an ultrasonic scan-ner in biomedical or nondestructive evaluation (NDE), or apassive array listening to a surveillance volume for passingairborne targets.

Here we consider the acoustic application of a laser ultra-sound experiment for the NDE of an aluminum part. Ourfirst approach is to apply the synthetic aperture focus tech-nique (SAFT) to image the part under investigation.13,14 We

Fig. 5. Model-based matched-field processor for acoustical imaging applications. Raw array field measurements and back-propagated model measurements are compared (decision function) creating a power image that is thresholded for detec-tion and localization.


assume that the flaws can be characterized by acoustic pointscatterers in the near-field. Therefore, spherical wave frontsimpinge on our measurement array emanating from theseflaws. The SAFT approach creates an image by assuming thatthe flaw location is at the given pixel, calculates the associat-ed propagation delays and attenuations assuming a homoge-neous medium, beamforms the measured data based on theseassumptions and estimates the power in the beam at theassumed location (pixel or point scatterer). This procedure isrepeated for each pixel until the observed power image isformed. Of course, this methodology can also be applied toimage the results of time-reversal focusing and decomposi-tion of the operator for localization purposes.15

Another more acoustics-oriented approach for imaging isbased on replacing the beamformer with a propagation model.The same scheme (as above) applies, but the propagation modelgenerates (backpropagation) the equivalent signal at the arrayand a criterion is created to “decide” whether a flaw is at a giventest location (pixel or point scatterer).7 The propagation modelcan be as sophisticated as deemed necessary incorporating fea-tures such as both compressional and shear waves, multipath,dispersion, and noise. This model-based technique is calledmatched-field imaging (MFI) and enables the acoustician to usethe a priori information available in a formal procedure to cre-ate the image.16,17 MFI is illustrated in Fig. 5 where we observethe measurements and propagation model generating the com-ponents of a decision function used to “detect” or “localize” theposition of a flaw (or target).7 Note that in the figure the plots areactual laser ultrasound array measurements. The object is a hole(flaw) drilled into an aluminum plate and measured using a syn-thetic aperture technique created for processing and detection.14

Consider a typical laser ultrasonic application where a NDEis performed on a rectangular aluminum part with two flaws.The SAFT and MFI images are shown in Fig. 6. We note that theMFI approach incorporates both compressional and shear wavefronts as well as the multipath caused by the part boundaries.The results of estimating the power at each pixel is shown wherewe see the high resolution and accurate results of the MFI com-pared to those of the SAFT processor.

Recursive (in-time) model-based processing for a towedacoustic array

Consider the following application taken from oceanacoustics to motivate the modern recursive model-basedapproach. Suppose we have a plane wave signal characterizingan acoustic source measured by a horizontally towed array. Theplane wave is at a 50 Hz temporal frequency and a bearing of 45o

impinging on a 2-element towed array at a 10 dB SNR with a towspeed of 5 m/sec. We would like to solve the problem of extract-ing the source bearing and temporal frequency parameters—thecritical information we seek. From the model-based perspective,the bearing/frequency estimation or equivalently, localizationproblem can be considered a problem of estimating a set ofparameters from noisy hydrophone measurements.18,19

The classical approach to this problem is to assume that thesignal is separable in space and time and select a single sensorchannel to perform spectral analysis/peak detection on the timeseries to estimate the temporal frequency parameter. The bear-ing can then be estimated independently by performing spatialspectral estimation (as before) or beamforming on the arraydata. A beamformer can be considered a spatial spectral estima-tor that is scanned over bearing angles indicating the true source

location at the bearing of maxi-mum power. The result of apply-ing this approach to our problemis shown in Fig. 7a. The figureillustrates the classical outputs ofboth spectral estimators peakingat the correct frequency and bear-ing angle parameters.

The MBP is implemented byincorporating the plane wavepropagation, hydrophone array,and noise models. However, thetemporal frequency and bearingangle parameters are unknownand must be estimated. The solu-tion to this problem is obtained byaugmenting the unknown param-eters into a MBP state-spacestructure and solving the so-called joint estimation problem.7

This is the parametrically adap-tive form of the MBP used inmost ocean acoustic applica-tions.18 Here the problembecomes nonlinear due to boththe measurement model (planewave) and the augmentation. It is

Fig. 6. Acoustical imaging of laser ultrasound flaw detection for NDE of aluminum part: (a) SAFT imaging; (b) model-basedmatched-field imaging; (c) thresholded SAFT image for flaw localization [(12.03 mm, 2.79 mm),(9.89 mm, 5.02 mm)]; (d)thresholded model-based matched-field image for flaw localization [(11.99 mm, 2.94 mm), (9.98 mm, 5.03 mm)].


more computationally intensive than the spectral estimatorsused in the classical approach; however, the results are appealingas shown in Fig. 7b. We see the bearing angle and temporal fre-quency estimates as a function of time converging to the truevalues of 50 Hz and 45o bearing angle. The MBP also producesthe “residual or innovations” sequence, (shown in the figure)that is used in determining its overall performance for valida-tion. In this case the sequence must be statistically zero-meanand white (uncorrelated) for optimal performance.7

Thus, the classical approach simply performs spectral esti-mation temporally and spatially (beamforming) to extract theparameters from noisy data, while the model-based approachembeds the unknown parameters into its propagation, measure-ment, and noise models enabling a solution to the joint estima-tion problem. The performance of the MBP is validated by ana-lyzing the statistics of its innovations sequence. This completesthe application.

Step 5: Model-based processing(distributed physical approach)

This step can be the most com-plex depending on the embeddedmodel representation. Typically, thephenomenology is represented by aset of partial differential equationscharacterizing the propagation medi-um and a set of noisy measurementequations that still can be character-ized by a state-space representation insome form or another. Whether theapplication is based on time-invariantstatistics like most of the applications

we have discussed or time/spacevarying (e.g., ocean) where weconstruct the processors usingrecursive-in-time or recursive-in-space techniques or both tocapture the ever-changing medi-um or motion of the acousticproblem that must be solved.

Model-based tomographicimaging for biomedicalimaging

Tomographic imaging isgoverned by partial differentialpropagation equations evolvingfrom a full-field wave model togenerate its solutions.20,21 It canbe thought of as a methodologyof solving an inverse problem.Consider the development of atomographic image of breast tis-sue to determine if a canceroustumor is or is not present. Thistechnology is based on Fourierimaging techniques and diffrac-tion tomographic reconstruc-

tion of the tissue using multiple scans through the breast(object). Fourier imaging essentially obtains projections inobject space using Fourier transforms (1 dimensional) to “fillin” regions in the 2 dimensional (2D) Fourier space and isbased on the Fourier diffraction theorem equating a projection(plane wave propagation) in object space to a region (arc) in2D-Fourier space. Once the space is filled, a 2D inversion isperformed using the model to perform a backpropagationsimilar to a numerical time-reversal to reconstruct the objectand create the image. This is similar to computer-aided tomo-graphic (CAT) reconstruction employing x-rays using theFourier slice theorem along a line, but here the acoustic prop-agation is modeled by the wave equation.20,21

The application of this model-based (distributed)approach to the breast tissue is shown in Fig. 8.22 Here weobserve the usual ultrasonic reflection image (not tomogra-

Fig. 7. Plane wave impinging on a 2-element hydrophone array: Frequency and bearing estimation problem: (a) classical spec-tral (temporal and spatial) estimation approach; (b) Model-based approach using parametrically adaptive (nonlinear)processor to estimate bearing angle, temporal frequency and the corresponding residual or innovations sequence.18,19

Fig. 8. Ultrasonic diffraction tomography is a model-based method based on the wave equation propagation model andbackpropagation techniques to construct a meaningful reconstruction. The model-based tomographic reconstructionshown on the far right image compares quite well to the usual ultrasonic scanner shown on the far left (reflection ultra-sound) and the x-ray CAT scan (middle).


phy) from a hospital scanner compared to an x-ray CATimage and finally the reconstructed image of the model-based processor using the embedded wave equation propaga-tion model. The results demonstrate the advantage of such asophisticated approach—especially for this application.

SummaryWe expressed the basic notion that signal processing is

concerned with the extraction of useful information fromuncertain measurement data. From this perspective, process-ing is an essential ingredient that the acoustician cannotignore and therefore must be included in a daily regimen forproblem solving. To explain the place that signal processingoccupies, we developed a conceptual signal processingframework to demonstrate how signal processing techniques“fit” into this plan. Using a “bottoms-up” perspective we illus-trated conceptually the progression up the so-called signalprocessing staircase (Fig. 1) to illustrate a variety of acousti-cal processing problems. We have discussed some of themodern techniques in acoustical signal processing employ-ing the philosophy that this approach incorporates more andmore of the a priori acoustical information available into theprocessing scheme that typically takes the form of a mathe-matical model. The incorporation of these models into theprocessor leads to the model-based approach or equivalently,the physics-based approach to signal processing. We startedwith a simple representation of the staircase showing that asthe models get more complex so does the processor usingsome simple examples for motivation. We demonstratedsome acoustic applications in sonar and nondestructive eval-uation and compared these results to the more classicalapproaches. We concluded the discussion with a tomograph-ic imaging technique demonstrating the evolution of model-based approaches to complex acoustical problems. Theanswer to the question of “science or science fiction” there-fore lies in the hands of the acoustician who must be able tosort through the processed results with the aid of statisticaltesting to assure the validity of the findings.AT

AcknowledgmentsThis work was performed under the auspices of the U. S.

Department of Energy by the Lawrence Livermore NationalLaboratory under Contract No. DE-AC52-07Na27344.

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York, 1997).

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5 M. Hayes, Statistical Digital Signal Processing and Modeling(John Wiley, New York, 1996).

6 J. V. Candy, “Modern techniques in acoustical signal and imageprocessing,” Proc. 9th Intl. Congress Sound & Vibration (2002).

7 J. V. Candy, Model-Based Signal Processing (John Wiley/IEEEPress, New Jersey, 2006).

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12 J. V. Candy and H. Jones, “Processing of prosthetic heart valvesounds for single leg separation classification,” J. Acoust. Soc.Am. 97(6), 3663–3673 (1995).

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14 J. V. Candy, R. D. Huber, D. H. Chambers and G. H. Thomas,“Matched-field imaging of laser generated ultrasound for non-destructive evaluation,” LLNL Report, UCRL-JC-133397 (1999).

15 M. Fink, “Time reversed acoustics,” Physics Today 50, 34–40 (1997).16 A. Baggeroer, W. Kuperman and H. Schmidt, “Matched-field

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18 J. V. Candy and E. J. Sullivan, “Ocean acoustic signal processing:a model-based approach.” J. Acoust. Soc. Am., 92(12),3185–3201 (1992).

19 E. J. Sullivan and J. V. Candy, “Space-time processing of a mov-ing array: A model-based approach.” J. Acoust. Soc. Am. 102(5),754–765 (1998).

20 A. J. Devaney, “A filtered backpropagation algorithm for diffrac-tion tomography,” Ultrasonic Imaging 4, 336–350 (1982).

21 A. C. Kak and M. Slaney, Principles of ComputerizedTomographic Imaging (IEEE Press, New York, 1988).

22 J. V. Candy, “Ultrasonic breast imaging program,” LLNL Report,UCRL-JC-124026 (1998).


James V. Candy is the Chief Scientist for Engineering andformer Director of the Center for Advanced Signal & ImageSciences at the University of California, Lawrence LivermoreNational Laboratory. Dr. Candy received his B.S.E.E. degreefrom the University of Cincinnati and his M.S.E. and Ph.D.degrees in Electrical Engineering from the University ofFlorida, Gainesville. He is an Adjunct Full-Professor at the

Jim and Pat Candy

University of California, Santa Barbara and a registeredControl System Engineer in the state of California. Dr.Candy is a Fellow of the Institute of Electrical and ElectronicsEngineers (IEEE) and the Acoustical Society of America(ASA) and was recently elected as a Life Member (Fellow) atthe University of Cambridge (Clare Hall College). He is amember of Eta Kappa Nu and Phi Kappa Phi honorary soci-eties and was elected as a Distinguished Alumnus by theUniversity of Cincinnati. Dr. Candy received the IEEEDistinguished Technical Achievement Award for the “devel-opment of model-based signal processing in oceanacoustics.” Dr. Candy was selected as an IEEE DistinguishedLecturer for oceanic signal processing. He was recently award-ed the prestigious Helmholtz-Rayleigh Interdisciplinary SilverMedal by the ASA “for his contributions to signal processingand ocean acoustics.” He has published over 200 journal arti-cles, book chapters, and technical reports as well as writtenthree texts in signal processing with a fourth in press. He iscurrently the IEEE Chair of the Technical Committee onSonar Signal and Image Processing and served as Chair of theASA Technical Committee on Signal Processing in Acousticsand as an Associate Editor for Signal Processing of JASAExpress Letters.


signal processing in acoustics: science or science … · lar application has led to many advances...

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