2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC) M17-46

An improved non-local means regularized iterative

reconstruction method for low-dose dental CBCT

J ia Hao, Li Zhang, Liang Li and Kejun Kang

Abstract-In clinical practice, the widespread use of dental

CBCT scanners has been limited because of cost, availability

and radiation dose considerations. The recently proposed non­

local means (NLM) method achieves excellent performance in

digital image denoising, which can also be used in low-dose

CBCT noise reduction. In this paper, we explore an improved

non-local means (INLM) regularized iterative reconstruction

method for low-dose CBCT with a low-mAs scanning protocol.

By using a pre-classification and similar block searching method,

the INLM filtering is more efficient than conventional NLM

method. Clinical experiments have been conducted and

demonstrate its performance in low-dose CBCT volume

reconstruction. Compared with FDK method, the proposed

method improves PSNR, image quality while preserves

structure and detail information in low-dose CBCT imaging.

Index Terms-dental CBCT, low-dose, non-local means,

iterative reconstruction algorithm

I. INTRODUCTION

I N clinical practice, the widespread use of dental CBCT scanners has been limited because of radiation dose

considerations. Generally, dose reduction can be achieved by reducing mAs, decreasing kVp, and even lowering the number of projections as compared to a normal dose scan. A simple but practical way is to acquire projection data with a lower mAs protocol, which has been widely utilized in clinical imaging. However, it leads to a degraded signal to noise ratio (SNR), due to a severe increase of the quantum and electronic noise. For decades, Radiologists have been struggling to balance image noise with radiation dose and noise reduction is one of the key technical problems.

The non-local means (NLM) filter proposed by Buades et al. [I] has emerged as a very simple and effective way to reduce noise while minimally affecting the original structures of the image. This new method takes advantage of the high degree of redundancy of the natural image, and proposes to replace the local comparison of pixels by the non local comparison of blocks. It brought in a new idea that if there are enough similar blocks in an image, they can be used for denoising by

Manuscript received November 15,2012. This work was supported in part by the grants from National Key Technology R&D Program of the Ministry of Science and Technology (No. 2012BA107B05) and grants from NNSFC 10905030 and Beijing Natural Science Foundation (Research on key techniques of medical cone-beam CT reconstruction from little data based on compressed sensing theory)

All the authors are with: I) Department of Engineering Physics, Tsinghua University, Beijing 100084, China. 2) Key Laboratory of Particle & Radiation Imaging (Tsinghua University), Ministry of Education, Beijing 100084, China

Zhang Li, Professor, Email: zli@maiI.tsinghua.edu.cn. Liang Li, Assistant Professor, Email: lIiang@tsinghua.edu.cn Hao Jia, PhD candidate, Email: haoj04@gmaiI.com

proper weighted average calculation. Soon it is applied t( noise reduction in medical images and demonstrated bette results than those of previous related methods [2]. Althougl the denoising effect and image quality are state-of-the-art, i is quite low to be practically realizable. The higl computational complexity is due to the cost of weight: calculation for all pixels in the image. Different improve< methods were researched. A basic idea here proposed is t( preclassity the image blocks according to fundamenta characteristics, such as their average gray values and gradien orientation. This is performed in a first path, and whill denoising in the second path, only blocks with simila characteristics are used to compute the weights [3].

Iterative methods are preferable in low-dose Cl reconstruction, including low-mAs scanning, under-samplin/ projection imaging and limited angle scanning. Under thl CS-based reconstruction framework, a priori sparsity propert: of the images could be utilized in iterative CTICBCl reconstructions through Total Variation (TV) minimizatiOl [4] or by using the prior images [5], which dramaticall: reduce the information required for reconstruction. Xu havi investigated a number of non-linear filters popular in thl image processing literature for their suitability in iterative Cl application, including bilateral filter, non-local means trilateral filter, total variation minimization. They conc1udl that NLM method performs best among the tested filters [6].

In this paper, we explore an iterative reconstructiOl

method regularized by an improved non-local means for low

dose CBCT with a low-mAs scanning protocol. By using pre

classification and similar searching methods, it is muc1

efficient than conventional NLM method. Only similar block

in the image are used in the weighted average calculation

Clinical experiments have been conducted and demon strati

its performance in low-dose CBCT volume reconstruction

The same dataset was also reconstructed by FDK method fo

comparison. The results show that this method perform

better in detail-preserving and improves the image quality

Compared with conventional NLM method, the propose<

INLM filtering algorithm leads to an overall reduction of thl

computational time by about 10 times (depends on thl

parameters and image to be reconstructed) in each iteratiOl

step.

978-1-4673-2030-6/12/$3\.00 ©2012 IEEE 3422

II. SYSTEM AND METHODOLOGY

A. Non local meanfilter Non-local means is a non-linear denoising filter. Rather

than the other filters using the local neighborhood, the NLM

estimates the denoised pixel NL(xi) as the mean of the

intensity values of all pixels whose Gaussian neighborhood

resembles the neighborhood of Xi within the image X . The

NLM can be formulated as:

NL(xJ = L wi.jXj (1) jEN(i) Here wi•j is the weight that measures the similarity of the

vectors X i and X j • The vectors denote a square

neighborhood of fixed size M x M, centered at pixels X i and X j' Theoretically, the search window N(i) can be as

large as the entire image. However, it is usually set to a

smaller window size to reduce the computational cost. The similarity is measured by a decreasing function of the

Gaussian-weighted Euclidean distance between X i and X j •

This distance is a L2 norm convolved with a Gaussian kernel

with standard deviation a . With this distance, Wij can be

written as:

W." =

_1 ex {_lie Xi - Xj )11�.a } " ZU) P h2 (2)

Here ZU) is the normalizing constant, which is given as:

II(Xi -xt>W Z(i) = " exp{- 2 2 ,a }

L.J, h (3)

Here the parameter h controls the degree of smoothness

and is usually selected empirically by users. As can be seen

from (2), it determines the decay of the exponential function

and thus the variation of the weight as a function of the

Euclidean distance. The NLM filter can be viewed as a

selective smoothing filter which gives increased weight to

pixels with similar neighborhood intensities. It can be

observed that when the centered pixel signal stands out from

its surrounding neighborhoods, the weight distribution is

heavily contributed by the pixel itself.

For a pixel located on a boundary, the weights are

distributed on the same curved line. For a pixel located in the

flat region, the weights are evenly distributed within the same

region. Therefore, the NLM is able to preserve a prominent

signal in a uniform background while smoothing out small

variations caused by noise.

B. improved Non-local Means algorithm The conventional NLM method has two major drawbacks

large computational time required by the process of distanci calculation in the whole image, especially on 3D volume data

every block in the image is used in the weighted averaging

no matter similar or dissimilar with the block to be denoised

which may lead some errors in a severely noisy image.

To overcome the drawbacks, an improved NLM algorithn

is used here. It is more efficient and achieves better denoisinl

results. The algorithm can be expressed as:

INLM(xJ = L wi/Xj (4 jE N (i),II,i, <£

Here only the similar blocks are used in the weighte(

averaging step. The similarity is evaluated by a giver

threshold £ . If Ik -,i/ II < £ , the two blocks can be considere(

similar. Otherwise it is considered dissimilar and ignored

Only the similar blocks are used in the weighting averagl

calculation.

Fig. 1. 1l1ustration of the similar block searching method in lNLM filtering.

To reduce the number of blocks taken into account in thl

searching, a pre-classification method is used. Considerinl

zero-mean noise, if the two estimated blocks are similar, the:

should have similar average gray values and standan

deviations. In this way, the maps of block means and standan

deviations are computed first. If they are located in a giver

region, the distance will be calculated. Otherwise the block:

are considered dissimilar and the distance is set to 00.

j IIXi-x/t E(x,) 2 var(x,) 2 - - ' <--< a <--<a deN N.) = L' , 171 E(-. ) 172, I

(- ) I

x' v Xi var Xj

00, otherwise

(5)

In this way, the maps of local means and local standan

deviations are precomputed in order to avoid repetitivi

calculations of moments for one same neighborhood. Thl

method can be speeded up by the pre-classification method a

most of the dissimilar blocks are ignored by this processing.

C. Reconstruction Algorithm In low-dose CBCT reconstruction, one way to cope wit!

the associated noise artifacts is to interleave a regularizatiOl objective into the iterative reconstruction framework. )

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Pre-classificatio n Similar block searching Weighted averaging r--------------------------- , ------------------------

1 Ilxi - x j II < 8 1---'-1 �.I INLM(x,) = I W'IXj 1

Fig.2 Flowchart of the TNLM filtering steps. The proposed TNLM method includes three major steps: pre-classification, similar block searching and weighted averaging.

popular method used in CT reconstruction is ASD-POCS algorithm proposed by Sidky. It alternates between a POCS step for constraint enforcement and TV minimization step. Motived by this design, each iteration step of the proposed reconstruction method consists of two phases: POCS and INLM filtering. Similar with [7], the image function is represented by use of conventional pixel basis functions and is

therefore described by a vector f . The knowledge of

projection data is represented by a vector g. Projection data

sample is Ndata • INLM(·) denotes the INLM filtering

processing proposed in the last section. The steps of the proposed algorithm can be summarized

as:

(a) Initialization:

n = 1,f[n, 1] = 0; (6)

(b) Data projection iteration, for m = 2 ... Ndata: - - - gi -M . f[ n m -1] f[n,m] = f[n,m -1] + M '- - ' (7) , M·M

(c) Positivity constraint 1 1

f[n] = {fj[n,NdataLf

.j[n,Ndata] ;::: 0

(8) 1 0, fj[n,Ndata] < 0 (d) Improved non-local means filtering

f' = INLM(f) (9)

(e) Initialize next loop

j[n+1,1]=1' (10)

The iteration is stopped when there is no appreciable change in the intermediate images after the POCS steps.

D. Experimental System A novel dental CBCT system (HiRes3D, LargeV

Corporation, Beijing China) is used in this experiment. It is

equipped an 13cm X 13cm amorphous silicon flat panel

detector. The pixel pitch achieves 127 J.l m. Using a 14-bit

depth ADC converter, a high contrast resolution is available.

The focal spot of the fixed anode X-ray tube used in this

system is 0.4 mm. The tube voltage is optional from 80kv to

100kv and the current can be adjusted from 2mA to 4mA.

There is a device to control the beam size and to limit the

irradiated volume. Using an offsetting detector scannin!

geometry, the system FOV is extended to 14cm X 8cm, wh icl

can cover the maxillofacial area. Rotation and date

acquisition time is about 20 seconds per scanning.

TIT. EXPERIMENTS AND RESULTS

The clinical datasets are collected using 100keV tubl

voltage and 3mA tube current. Reconstructed results an

shown in Figure.3-5. The reconstructed volume i

512x512x256. In this study, the sizes of Nand Min thl

INLM filter were set to 15x15 and 5x5. Two criteria are use<

to quantifY the performances of each method: the Peak Signa

to Noise Ratio (PSNR) and visual assessment.

As shown in Fig.3-5, the noise level of the reconstructe<

image using proposed method is perceptibly lower than thl

FDK reconstruction. This can be evaluated quantitatively b:

computing the PSNR in a selected ROT in the reconstruction

In the used dataset shown in Fig.5, using the propose<

reconstruction method, PSNR improves by 14.6% while thl

edge and detail information are well preserved. Compare<

with the conventional NLM method, the proposed INLM i

about 10 times faster in each iteration step, as most of thl

dissimilar blocks are ignored. The parameters in the propose<

method can be adjusted to achieve a better image quality or,

shorter computational time, which is a trade-off.

However, the complete iteration of proposed algorithn

consists of forwardlbackward projections and TNLM filtering

Therefore, the computation time is much longer than FDF

method. It can be enhanced substantially througl

parallelizing its implementation or using high performanci

computational hardware such as GPu.

Fig. 3. Reconstructed images from a dental CBCT system, the first one comes from FDK method and the second one comes from the proposed INLM regularized iterative method.

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Fig.4. Reconstructed images, the first one comes from FDK method and the second one comes from the INLM iterative method.

Fig.5. Reconstructed slices, the first one comes from FDK method and the second one comes from the proposed INLM regularized iterative method.

The convergence speed is also experimentally evaluated

using the clinical dataset. The curve of MSE value and

iteration number is shown in Fig.6. This method i

demonstrated robust by choosing proper parameters in thl INLM filtering.

MSE

°O�----��-===�'O�====� '5�====== 20�==--- 2�5------..J30 Fig. 6. The curve of MSE value versus number of iterations.

IV. CONCLUSION

In this paper, we use an improved non-local mean

regularized iterative reconstruction method for low-dosl dental CBCT, and compare the performance with FDK result

Clinical experiments demonstrate that this method improve

PSNR than FDK reconstruction and achieves better visua

quality. In additional, the low-contrast parts and detai

information are well preserved. Compared with conventiona

NLM method, the INLM filtering is much faster and practica

Clinical study has been conducted using a novel dental CBCl

system, and the reconstructions are presented, whicl

demonstrate its advantage in low-dose reconstruction.

We will future our study on optimization and acceleratiOl

of the algorithm, make it more efficient. Also it should bl

evaluated in spatial resolution, density contrast, an(

compared with the other state-of-the-art low-dosl

reconstruction methods, such as PWLS and ASD-POC�

methods.

REFERENCES

[I] A. Buades, B. Coli, and .I. M. Morel, "A Review of Image Denoisin, Algorithms, with A New One," Multiscale Model. Simul., vol. 4, no. 2, pr 490-530,2005.

[2] P. Coupe, P. Yger, S. Prima, et al. "An Optimized Blockwise Nonloca Means Denoising Filter for 3-D Magnetic Resonance Images. ", IEEI Trans. Med Imag. vol. 27, no. 4, pp. 425-441, April 2008.

[3] M. Mahmoudi and G. Sapiro. "Fast Image and Video Denoising vi; Nonlocal Means of Similar Neighborhoods," IEEE Signal Processin, Letters. Vol. 12, no.12, pp. 839-842,2005.

[4] E. Y. Sidky, C.-M. Kao, and X. Pan, "Accurate image reconstruction fron few-views and limited-angle data in divergent-beam CT," J. X-ray SCI Tech., vol. 14, pp. 119-139,2006

[5] G. Chen, .I. Tang and S. Leng. "Prior image constrained com pressel sensing (PICCS): A method to accurately reconstruct dynamic CT image from highly undersampled projection data sets ", Medical Physics, vol. 35 no.2, pp.660-663. 2008.

[6] W. Xu and K. Mueller "Evaluating Popular Non-Linear Image Processin, Filters for their Use in Regularized Iterative CT" Proc.IEEE MIC. pr 2864-2865,2010.

[7] E. Y. Sidky, X Pan. "Image reconstruction in circular cone-bean computed tomography by constrained, total-variation minimization," Phy, Med. BioI. Vol. 53, pp. 4777-4807, 2007.

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