EM-TV Methods for Inverse Problems with Poisson Noise

Sawatzky, Alex; Brüne, Christoph; Kösters, Thomas; Wübbeling, Frank; Burger, Martin

doi:10.1007/978-3-319-01712-9_2

Cited by 38 publications

(58 citation statements)

References 96 publications

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“…The FB-EM-TV method was recently introduced to solve emission tomography reconstruction problem (2) [7,8]. Its nested iteration scheme can be written as follows:…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Such approximation schemes (e.g. scheme (13)) cannot guarantee the theoretical convergence [8]. In contrast, the TV-PAPA does not need to perform an exact inner-optimization and it leads to a more practical algorithm.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Many efficient algorithms for TV-regularized optimization models were proposed, including expectation-maximization (EM)-based methods [5–8], projected quasi-Newton methods [9], primal-dual approaches [10], and fixed-point proximity algorithms [11–13]. In particular, a forward-backward splitting algorithm with nested EM-TV iteration scheme (FB-EM-TV) was recently developed in [7] for reconstruction of PET data with a low signal-to-noise ratio, and further justified and analyzed in [8].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, a forward-backward splitting algorithm with nested EM-TV iteration scheme (FB-EM-TV) was recently developed in [7] for reconstruction of PET data with a low signal-to-noise ratio, and further justified and analyzed in [8]. The FB-EM-TV was derived using the Karush-Kuhn-Tucker conditions, which formally provided the existence of a Lagrange multiplier such that the stationary points of the underlying model satisfied a certain coupled equation.…”

Section: Introductionmentioning

confidence: 99%

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Preconditioned alternating projection algorithm for solving the penalized-likelihood SPECT reconstruction problem

Zhang

Król

et al. 2017

Physica Medica

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Purpose The authors recently developed a preconditioned alternating projection algorithm (PAPA) for solving the penalized-likelihood SPECT reconstruction problem. The proposed algorithm can solve a wide variety of non-differentiable optimization models. This work is dedicated to comparing the performance of PAPA with total variation (TV) regularization (TV-PAPA) and a novel forward-backward algorithm with nested expectation maximization (EM)-TV iteration scheme (FB-EM-TV). Methods Monte Carlo technique was used to simulate multiple noise realizations of the fan-beam collimated SPECT data for a piecewise constant phantom with warm background, and hot and cold spheres with uniform activities at two noise levels. They were reconstructed using the aforementioned algorithms with attenuation, scatter, distance-dependent collimator blurring and sensitivity corrections. Noise suppressing performance, lesion detectability, lesion contrast, contrast recovery coefficient, convergence speed and selection of optimal parameters were evaluated. The conventional EM algorithms with TV post-filter (TVPF-EM) and Gaussian post-filter (GPF-EM) were used as benchmarks. Results The TV-PAPA and FB-EM-TV demonstrated similar performance in all investigated categories. Both algorithms outperformed TVPF-EM in terms of image noise suppression, lesion detectability, lesion contrast and convergence speed. We established that the optimal parameters versus information density approximately followed power laws, which offers a guidance in parameter selection for reconstruction methods. Conclusions For the simulated SPECT data, TV-PAPA and FB-EM-TV produced qualitatively and quantitatively similar images. They performed better than the benchmark TVPF-EM and GPF-EM, with only limited loss of lesion contrast.

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“…The FB-EM-TV method was recently introduced to solve emission tomography reconstruction problem (2) [7,8]. Its nested iteration scheme can be written as follows:…”

Section: Simulation Studiesmentioning

confidence: 99%

Section: Simulation Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Preconditioned alternating projection algorithm for solving the penalized-likelihood SPECT reconstruction problem

Zhang

Król

et al. 2017

Physica Medica

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“…Therefore, the image restoration problem is an essential task. Researchers have proposed many methods to deblur and denoise images; see [12,16,17,27,35,36,41,54] and references therein. In this paper, we focus on recovering images corrupted by blurring and Cauchy noise.…”

Section: Introductionmentioning

confidence: 99%

Cauchy Noise Removal by Nonconvex ADMM with Convergence Guarantees

et al. 2017

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Image restoration is one of the essential tasks in image processing. In order to restore images from blurs and noise while also preserving their edges, one often applies total variation (TV) minimization. Cauchy noise, which frequently appears in engineering applications, is a kind of impulsive and non-Gaussian noise. Removing Cauchy noise can be achieved by solving a nonconvex TV minimization problem, which is difficult due to its nonconvexity and nonsmoothness. In this paper, we adapt recent results in the literature and develop a specific alternating direction method of multiplier to solve this problem. Theoretically, we establish the convergence of our method to a stationary point. Experimental results demonstrate that the proposed method is competitive with other methods in visual and quantitative measures. In particular, our method achieves higher PSNRs for 0.5 dB on average.

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Performance of First-Order Algorithms for TV Penalized Weighted Least-Squares Denoising Problem

Sawatzky

2014

Lecture Notes in Computer Science

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Denoising of images perturbed by non-standard noise models (e.g., Poisson or Gamma noise) can be often realized by a sequence of penalized weighted least-squares minimization problems. In the recent past, a variety of first-order algorithms have been proposed for convex problems but their efficiency is usually tested with the classical leastsquares data fidelity term. Thus, in this manuscript, first-order state-ofthe-art computational schemes are applied on a total variation penalized weighted least-squares denoising problem and their performance is evaluated on numerical examples simulating a Poisson noise perturbation.

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EM-TV Methods for Inverse Problems with Poisson Noise

Cited by 38 publications

References 96 publications

Preconditioned alternating projection algorithm for solving the penalized-likelihood SPECT reconstruction problem

Preconditioned alternating projection algorithm for solving the penalized-likelihood SPECT reconstruction problem

Cauchy Noise Removal by Nonconvex ADMM with Convergence Guarantees

Performance of First-Order Algorithms for TV Penalized Weighted Least-Squares Denoising Problem

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