Tradeoffs Between Convergence Speed and Reconstruction Accuracy in Inverse Problems

Giryes, Raja; Eldar, Yonina C.; Bronstein, Alex; Sapiro, Guillermo

doi:10.1109/tsp.2018.2791945

Cited by 66 publications

(64 citation statements)

References 61 publications

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“…As suggested in [35], this convergence can be sped up by proposing a learned version of ISTA (LISTA). Furthermore, the authors of [38] demonstrated that the unfolded architecture facilitates a trade-off between fast convergence and reconstruction accuracy of the sparse recovery problem.…”

Section: Discussionmentioning

confidence: 99%

Deep Unfolded Robust PCA With Application to Clutter Suppression in Ultrasound

Solomon

Cohen

Zhang

et al. 2020

IEEE Trans. Med. Imaging

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179

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Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented subwavelength spatial resolution by relying on super-resolution techniques. A typical preprocessing step in super-resolution ultrasound is to separate the microbubble signal from the cluttering tissue signal. This step has a crucial impact on the final image quality. Here, we propose a new approach to clutter removal based on robust principle component analysis (PCA) and deep learning. We begin by modeling the acquired contrast enhanced ultrasound signal as a combination of a low rank and sparse components. This model is used in robust PCA and was previously suggested in the context of ultrasound Doppler processing and dynamic magnetic resonance imaging. We then illustrate that an iterative algorithm based on this model exhibits improved separation of microbubble signal from the tissue signal over commonly practiced methods. Next, we apply the concept of deep unfolding to suggest a deep network architecture tailored to our clutter filtering problem which exhibits improved convergence speed and accuracy with respect to its iterative counterpart. We compare the performance of the suggested deep network on both simulations and in-vivo rat brain scans, with a commonly practiced deep-network architecture and the fast iterative shrinkage algorithm, and show that our architecture exhibits better image quality and contrast.

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Section: Discussionmentioning

confidence: 99%

Deep Unfolded Robust PCA With Application to Clutter Suppression in Ultrasound

Solomon

Cohen

Zhang

et al. 2020

IEEE Trans. Med. Imaging

Self Cite

179

171

View full text Add to dashboard Cite

show abstract

“…Yet, for sophisticated priors iterative optimization schemes are inevitable, and the regularization parameter has an effect which is similar to the step size in these schemes. In such cases, extremely low value of β inherently results in a massive slowdown in the convergence for convex priors [40], [41] and/or bad local minima for nonconvex priors. Taking a numerical optimization point of view, in the sequel we empirically show thatx BP is superior tox LS even for 2 priors with β → 0, if few iterations of conjugate gradients are used instead of the closed-form expressions (16) and (17).…”

Section: B Performance Analysismentioning

confidence: 99%

Back-Projection Based Fidelity Term for Ill-Posed Linear Inverse Problems

Tirer

Giryes

2020

IEEE Trans. on Image Process.

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Ill-posed linear inverse problems appear in many image processing applications, such as deblurring, superresolution and compressed sensing. Many restoration strategies involve minimizing a cost function, which is composed of fidelity and prior terms, balanced by a regularization parameter. While a vast amount of research has been focused on different prior models, the fidelity term is almost always chosen to be the least squares (LS) objective, that encourages fitting the linearly transformed optimization variable to the observations. In this work, we examine a different fidelity term, which has been implicitly used by the recently proposed iterative denoising and backward projections (IDBP) framework. This term encourages agreement between the projection of the optimization variable onto the row space of the linear operator and the pseudoinverse of the linear operator ("back-projection") applied on the observations. We analytically examine the difference between the two fidelity terms for Tikhonov regularization and identify cases where the new term has an advantage over the standard LS one. Moreover, we demonstrate empirically that the behavior of the two induced cost functions for sophisticated convex and nonconvex priors, such as total-variation, BM3D, and deep generative models, correlates with the obtained theoretical analysis.

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“…22 Images labeled with 'difference' indicate the difference between the output image generated from the corresponding SR algorithm and the original image. Similar performance was observed for other MNIST or OMNIGLOT images.We used the GFLSTM network for DNN f θ (·) in TSN and trained the network using Algorithm 1, whose input tuple (k 1 , k 2 , s d , s b , n e , v SNRdB ) was set to (1, 250, 6 · 10 5 , 250, 400,20). Note that DNN f…”

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confidence: 99%