reconstruction of sectional images in frequency-domain based photoacoustic imaging

Reconstruction of sectional images in frequency-

domain based photoacoustic imaging

Banghe Zhu* and Eva M. Sevick-Muraca

Center for Molecular Imaging, The Brown Foundation Institute of Molecular Medicine, The University of Texas

Health Science Center at Houston, Houston, Texas 77030, USA *[email protected]

Abstract: Photoacoustic (PA) imaging is based upon the generation of an

ultrasound pulse arising from subsurface tissue absorption due to pulsed

laser excitation, and measurement of its surface time-of-arrival. Expensive

and bulky pulsed lasers with high peak fluence powers may provide

shortcomings for applications of PA imaging in medicine and biology.

These limitations may be overcome with the frequency-domain PA

measurements, which employ modulated rather than pulsed light to generate

the acoustic wave. In this contribution, we model the single modulation

frequency based PA pressures on the measurement plane through the

diffraction approximation and then employ a convolution approach to

reconstruct the sectional image slices. The results demonstrate that the

proposed method with appropriate data post-processing is capable of

recovering sectional images while suppressing the defocused noise resulting

from the other sections.

©2011 Optical Society of America

OCIS codes: (170.2655) Functional monitoring and imaging; (170.5120) Photoacoustic

imaging; (170.6960) Functional monitoring and imaging; (170.3660) Light propagation in

tissues.

References and Links

1. X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Non-invasive laser-induced photoacoustic

tomography for structural and functional imaging of the brain in vivo,” Nat. Biotechnol. 21(7), 803–806 (2003).

2. H. P. Brecht, R. Su, M. Fronheiser, S. A. Ermilov, A. Conjusteau, and A. A. Oraevsky, “Whole-body three-

dimensional opto-acoustic tomography system for small animals,” J. Biomed. Opt. 14(6), 064007 (2009).

3. D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral

opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).

4. Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom

studies in a spherical scanning geometry,” Phys. Med. Biol. 54(18), 5457–5467 (2009).

5. L. V. Wang, “Prospects of photoacoustic tomography,” Med. Phys. 35(12), 5758–5767 (2008).

6. L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509

(2009).

7. B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength

photoacoustic images,” J. Opt. Soc. Am. A 26(2), 443–455 (2009).

8. L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum

Electron. 14(1), 171–179 (2008).

9. B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic

wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).

10. N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” J. Acoust. Soc. Am. 123(5),

2577–2590 (2008).

11. A. Petschke and P. J. La Rivière, “Comparison of intensity-modulated continuous-wave lasers with a chirped

modulation frequency to pulsed lasers for photoacoustic imaging applications,” Biomed. Opt. Express 1(4),

1188–1195 (2010).

12. K. Maslov and L. V. Wang, “Photoacoustic imaging of biological tissue with intensity-modulated continuous-

wave laser,” J. Biomed. Opt. 13(2), 024006 (2008).

13. U. Schnars and W. P. O. Jutner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci.

Technol. 13(9), R85–R101 (2002).

14. X. Zhang, E. Y. Lam, and T. C. Poon, “Reconstruction of sectional images in holography using inverse

imaging,” Opt. Express 16(22), 17215–17226 (2008).

#152622 - $15.00 USD Received 14 Sep 2011; revised 4 Oct 2011; accepted 5 Oct 2011; published 1 Nov 2011(C) 2011 OSA 7 November 2011 / Vol. 19, No. 23 / OPTICS EXPRESS 23286

15. E. Y. Lam, X. Zhang, H. Vo, T. C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional

image reconstruction using optical scanning holography,” Appl. Opt. 48(34), H113–H119 (2009).

16. Z. Yuan, C. Wu, H. Zhao, and H. Jiang, “Imaging of small nanoparticle-containing objects by finite-element-

based photoacoustic tomography,” Opt. Lett. 30(22), 3054–3056 (2005).

17. Z. Yuan, Q. Wang, and H. Jiang, “Reconstruction of optical absorption coefficient maps of heterogeneous media

by photoacoustic tomography coupled with diffusion equation based regularized Newton method,” Opt. Express

15(26), 18076–18081 (2007).

18. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive

measurement of tissue optical properties,” Appl. Opt. 28(12), 2331–2336 (1989).

19. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, “Quantitation of time- and frequency-resolved

optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195(2), 330–351 (1991).

20. F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain

fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187(2), 597–619 (2003).

21. P. Baluk, J. Fuxe, H. Hashizume, T. Romano, E. Lashnits, S. Butz, D. Vestweber, M. Corada, C. Molendini, E.

Dejana, and D. M. McDonald, “Functionally specialized junctions between endothelial cells of lymphatic

vessels,” J. Exp. Med. 204(10), 2349–2362 (2007).

22. J. C. Rasmussen, I. C. Tan, M. V. Marshall, C. E. Fife, and E. M. Sevick-Muraca, “Lymphatic imaging in

humans with near-infrared fluorescence,” Curr. Opin. Biotechnol. 20(1), 74–82 (2009).

23. C. Kim, K. H. Song, F. Gao, and L. V. Wang, “Sentinel lymph nodes and lymphatic vessels: noninvasive dual-

modality in vivo mapping by using indocyanine green in rats--volumetric spectroscopic photoacoustic imaging

and planar fluorescence imaging,” Radiology 255(2), 442–450 (2010).

24. A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics

equations,” J. Comput. Phys. 220(1), 441–470 (2006).

25. Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite

element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular

imaging,” Phys. Med. Biol. 55(16), 4625–4645 (2010).

26. H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol.

55(4), 947–962 (2010).

27. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J.

Opt. Soc. Am. A 27(7), 1630–1637 (2010).

1. Introduction

In recent years photoacoustic (PA) imaging has experienced rapid development in the

biophotonics community [1–7]. PA takes the advantage of both the optical and ultrasonic

imaging modalities, promising high-resolution structural and functional imaging of tissue [8].

Pulsed lasers are generally used to induce ultrasonic waves that originate from transient

absorption of the propagating light pulse creating a local tissue expansion. The local

expansion generates an ultrasonic pulse that travels to the tissue interface for facile detection.

The pressure of PA wave is detected by ultrasound transducers positioned outside or on the

surface of tissue and can be used to reconstruct the origin of the initial PA pulse. The

technique is thus suitable for quantifying tissue properties or identifying pathological

structures. PA has been demonstrated to image the blood vasculature in both small animals

and humans via high resolution [9]. However, time-domain PA requires a short laser pulses in

order to fulfill the assumptions upon which PA imaging is based [10]. In addition, expensive

and bulky pulsed lasers with high peak powers can limit time-domain PA applications in

medicine and biology.

Frequency-domain (FD) based PA methodologies may offer an attractive alternative

measurement scheme although its signal-to-noise ratio (SNR) is 20dB - 40 dB worse than that

of pulse system [11, 12]. In this approach, instead of a pulse of laser light, the tissue or object

surface is illuminated with intensity-modulated continuous-wave (CW) laser or laser diode as

an excitation source. Generally the modulation frequency in FD-based PA imaging system is

scanned over the frequency range of interest to preserve full axial (depth) resolution, but this

method may be time-consuming and can complicate instrumentation. Recently, a single-

frequency detection using amplitude-based axial resolution has been demonstrated for

imaging subsurface blood vessels in tissues [12]. However, in order to localize the PA sources

one needs to sweep the modulation frequency within the bandwidth of ultrasonic transducer.

Herein we propose a convolution approach for the reconstruction of sectional images in

FD based PA imaging using the complex information (i.e. both amplitude and phase). In our


method, the PA pressure on the measurement plane is modeled using diffraction

approximation and the inversion is implemented by performing the convolution operation and

appropriate post-processing. This approach is similar to digital holography [13–15], and is the

first time, to the best our knowledge, to be introduced to the FD based photoacosutic

tomography. In comparison to digital holography PA based methods have a significant

advantage in that the ultrasound amplitude attenuation is two orders of magnitude less than

that of a propagating light imaging, allowing the acoustic waves to travel long distances in

tissue without significant distortion or attenuation. Thus, the technique may be especially

suitable to image deep biological tissues if incident fluence rates can be reasonably controlled

and interference from other light absorbing structures not within the focus plane can be

accounted for. To remove the defocused noise from the other sections, only real part of the

reconstructed sectional image was used. Then the finding of maximum focus measure instead

of sweeping modulation frequency was applied to determine the depth information. Combined

with the light propagation model in tissue, the absorption coefficients of blood vessels can be

quantitatively retrieved, making it possible for functional imaging.

2. Methods

2.1 Photoacoustic wave equation

In the frequency domain, the generation and propagation of laser-induced acoustic wave

through highly scattering media (such as biological tissue) can be described by the following

Helmholtz-like equation [10, 16, 17]:

( ) ( )( )

( )2 2 0

0 0, ,

p

c rp r k p r ik A r

C

βω ω

Φ∇ + = = Φ

(1)

where p is the pressure wave; 0 0

/k cω= is the wavenumber related to the angular frequency

ω and the speed of the acoustic wave 0

c in the tissue; β is the isobaric volume expansion

coefficient; p

C is the specific heat; Φ is the absorbed light energy density that is the product

of the optical absorption coefficient, a

µ , and optical fluence, Ψ (i.e. a

µΦ = Ψ ); and

0

0

p

ckA i

C

β= . To recover the optical absorption coefficient

aµ from the pressure wave

( ),p r ω

, the distribution of photon fluence Ψ in scattering media is required.

2.2 Light propagation in scattering media

The gold standard for describing light propagation in turbid media is the radiative transport

equation (RTE). However, a direct solution of RTE is a challenging task even with high

performance computers. Instead, an approximation to the radiative transport equation is used

and has been accomplished in biological tissues [18]. In this approximation, the multiply

scattered light intensity is described by the diffusion equation, which is given in the frequency

domain over a 3D bounded domain Ω by [19, 20]

( )D k S on−∇ ∇Ψ + Ψ = Ωi

(2)

and subject to the Robin boundary conditions on the domain boundary ∂Ω of

( ) 0n D b on∇Ψ + Ψ = ∂Ωi

(3)


where the excitation source S is intensity modulated at angular frequency ω and propagates

through medium resulting in the complex photon fluence Ψ ; a

ik

c

ωµ= + is the decay

coefficient described by the angular frequency ω and the speed of light c in the tissue; the

optical diffusion coefficient D is given by ( )'1/ 3 ,a sD µ µ= + where '

sµ is the reduced optical

scattering coefficient; and the Robin boundary coefficient b is governed by the reflection

coefficient R range from 0 (no reflectance) to 1 (total reflectance), ( )( )1

.2 1

Rb

R

−=

+

2.3 Reconstruction of sectional images by the convolution approach

The PA wave on the measurement plane ( ), , 0x y z = can be expressed as the assembly of the

spherical waves which converge at the different points ( , , )zζ η within the tissue. The

measured acoustic wave ( ), ,p x y ω can be computed by the diffraction formula:

( ) ( ) ( ), , , , , , , ,p x y A z g x y z d d dzω ζ η ζ η ζ η

+∞

−∞= Φ∫∫ ∫ (4)

where the impulse response ( )g , , , ,x y zζ η originating from ( , , )zζ η and detected at ( , )x y is

given by

( )( ) ( )

( ) ( )

2 22

2 22

2exp

, , , ;

i z x yi

g x y z

z x y

πζ η

λζ ηλ ζ η

− + − + − =+ − + −

(5)

where λ is the wavelength of the acoustic wave. The mathematical approach was first applied

for numerical reconstruction of suboptical holography and later for optical holograms [13].

Since Eq. (5) represents a shift-invariant linear system characterized by

( ) ( )g , , , g , ,x y x yζ η ζ η= − − the diffraction integral is a convolution. For discretized

sectional images, z can be denoted by 1 2, ,....,

Mz z z and the PA pressure wave on the

measurement plane ( , )x y can be represented by a summation:

( ) ( )

1, , ( ) , ,

M

mmp x y A g x y zω

== Φ⊗∑

(6)

where ( ) 2 2 2 2 2 22, ; exp

m m m

ig x y z i z x y z x y

πλ λ

= − + + + + ; and ⊗ represents the

convolution operator. The impulse response function, g, has a different form compared to that

from sweeping modulation frequency and also the convolution is operated in the space

domains x and y , not the space domain z described in the reference [12].

2.4 Data post-processing

Suppose the focused plane is located at 1

z , as shown in Fig. 1. A reconstruction of this

sectional image requires recovering ( )1Φ , ,A zζ η from the PA wave of ( ), , .p x y ω The

conventional approach to obtain sectional images involves computing the convolution of PA

wave with the conjugate of the impulse response *( )g at the focused position 1

z :


( ) ( )

( ) ( )

*

1 1

*

12

( ) , , , ,

, , , ,M

mm

p g z A z

A z g z

ζ η ζ η

ζ η ζ η=

⊗ = Φ

+ Φ ⊗∑ (7)

The first term above represents the focused section at 1

z and the second term refers to as

the defocused noise contributed by acoustic waves generated at the other sections. Hence, the

reconstructed sectional image is a mixed distribution of the focused image points and the

defocused noise. The reconstructed sectional image will be blurred by different degrees

depending on the strength and distance of contributing sources from the focused section. Note

also that the first term in Eq. (7) can be regarded as real due to the negligible phase shift of

exciting laser light (see the numerical simulation section), while the second term is complex.

By retaining the real part of Eq. (7), the imaginary part of the defocused noise will be

completely removed since it contains no meaningful signal content at the focus plane.

Suppose a section located at 1

z depth contains blood vessels with orders of magnitude larger

absorption than other tissue sections, and the maximum absorbed optical energy density

would be deposited at the 1

z section. With the proposed convolution approach, the maximum

absorbed optical energy density is reconstructed at the 1

z section. By projecting the maximum

reconstructed absorbed light energy density along the z direction, the 1

z depth information

can be obtained. Combined with the light propagation model, the map of optical absorption

coefficient may be recovered. Figure 2 shows a block diagram of reconstruction of sectional

images in the FD based photoacoustic imaging process.

Fig. 1. Coordinate system for the measurement plane and slab tissue.


Fig. 2. Schematic of single frequency based photoacoustic tomography process, where “Re”

represents the real part.

3. Numerical simulations

As for the evaluation of the excitation fluence distribution, we assume a simple case of a slab

tissue shown in Fig. 1 that can later be modified for different geometries. Simulated data of

fluence was acquired on a 1.28 x 1.28 x 2.0 cm3 domain. The slab tissue was modeled as

homogeneous with the following values: absorption coefficient a

µ of 0.02 cm−1

; reduced

scattering coefficient 's

µ of 10.0 cm−1

; reflection coefficient of 0.433 on the top surface and

0 on all other surfaces. While more complicated and informative sources such as patterned

modulated incident light could be used, a homogeneously distributed area source modulated at

50MHz was simulated to illuminate the top surface of the chosen domain. Figure 3 shows the

calculated complex photon fluence at the excitation wavelength of 785 nm as a function of

depth, computed using finite element method. We can see from Fig. 3 that the amplitude of

the complex photon fluence decreases exponentially and its phase increases slowly with

respect to the depth. When compared to the acoustic wave phase delay shown below, the

initial phase value of the induced PA wave can be assumed to be zero. For the pressure wave

measurements, the slab tissue and the acoustic transducer are immersed in water and the

distance between the top surface of the slab tissue and the measurement plane is 4.0 cm, as

shown in Fig. 1.


Fig. 3. Normalized amplitude and phase of complex photon fluence as a function of distance

from the top surface of the slab tissue.

Reconstruction was performed on a domain of interest divided into 20 sections ( 20)M = ,

where two distinct sections, 16

4.8z = cm and 18

4.9z = cm away from 0z = measurement

plane, include absorptive targets mimicking blood vessels with optical absorption coefficient

of 3.0 (cm−1

). For these numerical simulations, the coefficient 0

0

p

ckA i

C

β= in Eq. (1) is set to

1 for simplicity. Figure 4(a) and 4(b) present the normalized amplitude and phase of the

simulated acoustic pressure field on the measurement plane, respectively, from which it is

difficult to decipher the structure of blood vessels. Gaussian noise of 20 dB was first added to

the simulated PA pressure to simulate experimentally measured data. The reconstructed 3D

map was sampled in intervals of 100 mµζ η∆ = ∆ = , which defines transverse resolution in

the ζ and η directions, respectively, and a longitudinal sampling interval of 500 mµ , which

defines resolution in the z direction.

Fig. 4. Normalized amplitude (a) and phase (b) of photoacoustic wave on the measurement plane.

(a) (b)


Figure 5(a) and 5(b) show the reconstructed sectional images at 16

4.8z = cm and

184.9z = cm, respectively, without data post-processing. Their corresponding absorptive

coefficient profiles through 0.8ζ = cm are shown in Fig. 5(c) and 5(d), respectively. The

figures show that the absorption coefficients of simulated blood vessels are clearly

reconstructed in the corresponding focused sections. We can also observe the strong

defocused noise originating from the interference in sections adjacent to the focused sections.

Fig. 5. Reconstructed sectional images of the blood vessels using convolution approach at two

different depths: (a) 16

4.8z = cm and (b)18

4.9z = cm. Their corresponding absorptive

coefficient profiles through 0.8ζ = cm indicating the shifted initial optical absorption

coefficient (blue dash line) and reconstruction (red solid line) are shown in (c) and (d),

respectively.

With the data post-processing, the reconstructed focused sections are weakly influenced

by the defocused noise, as shown in Fig. 6. Figure 7 shows the reconstructed sectional image

at depth 11

55 4.z = cm which contains no blood vessels and the similar resutls are obtained

for other sections. The C-scan or en face images (a gray-scale plot of adding all the

reconstructed sectional images) are shown in Fig. 8, from which we can see that optical

absorption coefficients of blood vessels have been reconstructed properly.

Focused

blood vessels Defocused

blood vessels

Defocused

blood vessels Focused

blood vessels

(a) (b)

(c) (d)


Fig. 6. Reconstructed sectional images of the blood vessels using convolution approach along

with data post-processing at two different depths: (a) 16

4.8z = cm and (b)18

4.9z = cm.

Their corresponding absorptive coefficient profiles through 0.8ζ = cm indicating the shifted

initial optical absorption coefficient (blue dash line) and reconstruction (red solid line) are

shown in (c) and (d), respectively.

Fig. 7. Reconstructed sectional image of the surrounding tissues using convolution approach

along with data post-processing at depth 11

55 4.z = cm (a). The corresponding absorptive

coefficient profiles through 0.8ζ = cm indicating the shifted initial optical absorption

coefficient (blue dash line) and reconstruction (red solid line) are shown in (b).

(a) (b)

(a) (b)

(c) (d)


Fig. 8. The C-scan or en face images of the reconstructed blood vessels (a) and its

corresponding absorptive coefficient profiles through 0.8ζ = cm indicating the shifted initial

optical absorption coefficient (blue dash line) and reconstruction (red solid line) (b).

As a complementary of the blood vasculature, the lymphatic circulatory system returns

water and proteins from various tissues back to the bloodstream. The lymphatics can be

imaged using fluorescence optical microscopy [21], and near-infrared fluorescence imaging

[22], and photoacoustic imaging [23], through intradermal injection of vital dye such as

indocyanine green (ICG). With the administration of dye, the lymphatic vessels may have

high optical absorption coefficients compared to the blood vessels. Figure 9(a) and 9(b) show

the reconstructed optical coefficient coefficients of blood vessels with a

µ of 3.0 cm−1

located

at 4.8 cm and lymphatic vessels witha

µ of 30.0 cm−1

located at 4.9 cm, respectively. Their

corresponding profiles through 0.8ζ = cm are shown in Fig. 9(c) and 9(d), respectively. The

corresponding C-scan or en face images are shown in Fig. 10, from which we can see that

both the blood vessels and lymphatic vessels were reconstructed simultaneously. Similar

simulation results can be obtained under other modulation frequencies.

(a) (b)


Fig. 9. Reconstructed sectional images of the blood vessels located at 16

4.8z = cm (a) and

lymphatic vessels located at 18 4.9z = cm (b) using convolution approach along with data post-

processing. Their corresponding absorptive coefficient profiles through 0.8ζ = cm indicating

the shifted initial optical absorption coefficient (blue dash line) and reconstruction (red solid

line) are shown in (c) and (d), respectively.

Fig. 10. The C-scan or en face images of the reconstructed blood and lymphatic vessels (a) and

its corresponding absorptive coefficient profiles through 0.8ζ = cm indicating the shifted

initial optical absorption coefficient (blue dash line) and reconstruction (red solid line) (b).

4. Discussion

As for the acoustic diffraction theory, it is reasonable by employing a small size transducer

with relative large distance from the object and immersing the transducer and the imaging

(a) (b)

(a) (b)

(c) (d)

Reconstructed

blood vessels

Reconstructed

lymphatic vessels


domain in water. In addition, the acoustic pressure, as given in Eq. (4), does not consider the

photonic and thermal contributions to the system. This implies that the thermal and acoustic

confinements are satisfied. It should be noted that both the thermal and stress confinements

can be measured by the ratios of the squared photonic to the thermal and acoustic wave

numbers, respectively [10]. For the parameters given in the numerical simulations as well as

the typical thermal diffusivity of soft tissue as 0.11mm2/s and the speed of light in tissue is on

the order of 2 x108 m/s, the calculated ratios of the photonic to the thermal and acoustic wave

numbers are small and it follows that the thermal subsystem has little effects on the

measurements [10]. If acoustic attenuation in tissue is not negligible, one may need to modify

the photoacoutic wave Eq. (1). As photons experience attenuation in tissue, the photonic

contribution becomes negligible and only the acoustic contribution remains at a large

distance. Otherwise, one needs to consider the photonic contribution by modifying the

impulse response, ( )g , , , ,x y zζ η . To obtain more accuracy distribution of photon fluence in

biological tissues, high order spherical harmonics and simplified spherical harmonics models

may be used to solve the RTE [24, 25]. On the other hand, using the Monte Carlo simulation

to solve the RTE, one can obtain any desired accuracy [26].

In numerical simulations, we assume that the blood vessels at different sections are not

overlapped along the z direction and thus this technique is suitable for imaging the shape of

tissue of object. If the blood vessels overlap along z direction, based on the proposed

convolution method with data post-processing techniques, the blood vessel with the maximum

absorbed optical energy density in z direction would be constructed. The proposed approach

is direct and fast. If one wants to reconstruct the overlapping structures, the Wiener filter

approach, the Wigner distribution function approach and the inversion methods used in the

field of optical scanning holography [14-15, 27] can be adapted and applied to the

photoacoustic imaging. Both the Wiener filter and Wigner distribution function approaches

work well for only two sections. In addition, the Wiener filter approach requires no noise

virtually introduced in the imaging system, and the imaging reconstruction is a time-

consuming process for the Wigner distribution approach. Fortunately, inverse imaging

approaches, such as the conjugate-gradient based algorithm with Tikhonov regularization, are

more effective in suppressing noise and retrieving the multiple sections. However, the sharp

edges become blurred in the reconstructed sections, due to minimizing the total energy in the

reconstruction algorithm. With the total-variation regularization and a nonnegativity

constraint, the sharp edges can be well preserved in the reconstructed sections using a primal-

dual Newton’s method combined with gradient projection. The minimum separation between

two sections depends on the modulation frequency, SNR and the sampling size in the z

direction. For our experimental conditions, two sections with minimum separation of

500 mµ can be reconstructed.

In summary, we demonstrate that the distributions of the optical absorption are possibly to

be reconstructed using the convolution approach with appropriate data post processing

coupled with optical diffusion equation in the FD based PA imaging.


reconstruction of sectional images in frequency-domain based photoacoustic imaging

Documents