Accurate EM-TV algorithm in PET with low SNR

Sawatzky, Alex; Brüne, Christoph; Wübbeling, Frank; Kösters, Thomas; Schäfers, Klaus P.; Burger, Martin

doi:10.1109/nssmic.2008.4774392

Cited by 96 publications

(102 citation statements)

References 14 publications

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“…Here, we are confronted with speckle noise [40], which is usually assumed to follow a Gamma distribution. In electronic microscopy [45], single particle emission computed tomography (SPECT) [51] and positron emission tomography (PET) [56], non-additive Poisson noise appears in connection with blur. In this paper, we focus on Gamma distributed noise although our model is appropriate for Poisson noise as well.…”

Section: Introductionmentioning

confidence: 99%

“…However, in deblurring problems, where we have frequently Poisson noise, Csiszár's I-divergence [20] is usually applied as data fitting term. For the expectation-maximization (EM) approach related to the I-divergence model in deblurring problems see [49,52] and the references therein and for the EM -total variation (TV) model we refer to [51,56]. NL-means filters for removing non-additive noise were examined in [19,43].…”

Section: Introductionmentioning

confidence: 99%

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Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

2009

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In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer for removing multiplicative Gamma noise. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizers of our restoration functionals by applying Douglas-Rachford splitting techniques, resp. alternating direction methods of multipliers. For a particular splitting, we present a semi-implicit scheme to solve the involved nonlinear systems of equations and prove its Q-linear convergence. Finally, we demonstrate the performance of our methods by numerical examples.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

2009

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“…Although ART-SB is a state-of-the-art "shrinkage methodology," [12][13][14][16][17][18] it provides a solution for l 1 -regularized problems, minimizing TV by means of the SB method introduced by Ref. 19.…”

Section: Discussionmentioning

confidence: 99%

“…These alternate an iterative method (such as simultaneous ART or the expectation-maximization algorithm) with a denoising step in order to minimize the TV and thus obtain enhanced results in computed tomography and positron emission tomography. [16][17][18] Johnston et al and Pan et al 16,17 used a standard gradient descent method, whereas Sawatzky 18 applied a dual approach to minimize the TV functional. Consequently, the choice of technique for solving l 1 regularization-based problems may become crucial, as l 1 is nonlinear; therefore, the computational burden can increase significantly using classic gradient-based methods.…”

Section: Introductionmentioning

confidence: 99%

Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography

et al. 2013

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Abstract. Fluorescence diffuse optical tomography (fDOT) is a noninvasive imaging technique that makes it possible to quantify the spatial distribution of fluorescent tracers in small animals. fDOT image reconstruction is commonly performed by means of iterative methods such as the algebraic reconstruction technique (ART). The useful results yielded by more advanced l 1 -regularized techniques for signal recovery and image reconstruction, together with the recent publication of Split Bregman (SB) procedure, led us to propose a new approach to the fDOT inverse problem, namely, ART-SB. This method alternates a cost-efficient reconstruction step (ART iteration) with a denoising filtering step based on minimization of total variation of the image using the SB method, which can be solved efficiently and quickly. We applied this method to simulated and experimental fDOT data and found that ART-SB provides substantial benefits over conventional ART.

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“…Le et al proposed to minimize (3) by using a traditional gradient descent, which is slow. More efficient methods were proposed later: Sawatzky et al [30] proposed an EM-TV algorithm; Chaux et al [31] proposed a nested iterative algorithm; Setzer et al [28] employed the split Bregman technique [32]; Figueiredo et al [14] used the alternating direction method of multiplier to solve (3) or a frame-based version of (3). Based on the developments mentioned above and inspired by the K-SVD algorithm for Gaussian noise removal, we here propose a new model, involving a sparse representation over a learned dictionary, to deblur images corrupted by Poisson noise.…”

Section: Introductionmentioning

confidence: 99%

A Dictionary Learning Approach for Poisson Image Deblurring

Moisan

et al. 2013

IEEE Trans. Med. Imaging

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The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a Maximum A Posteriori (MAP) formulation, recently sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, we propose in this paper a model containing three terms: a patch-based sparse representation prior over a learned dictionary, the pixel-based total variation regularization term and a data-fidelity term capturing the statistics of Poisson noise. The resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting. Extensive experimental results suggest that in terms of visual quality, PSNR value and the method noise, the proposed algorithm outperforms state-of-the-art methods

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Accurate EM-TV algorithm in PET with low SNR

Cited by 96 publications

References 14 publications

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography

A Dictionary Learning Approach for Poisson Image Deblurring

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