Deep Learning of truncated singular values for limited view photoacoustic tomography

Schwab, Johannes; Antholzer, Stephan; Nuster, Robert; Paltauf, Guenther; Haltmeier, Markus

doi:10.1117/12.2508418

Cited by 16 publications

(17 citation statements)

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“…For that purpose, we compare classical truncated SVD, the data-driven extended SVD and the null-space approach of [21]. Similar results are presented in [22] for the limited data problem of photoacoustic tomography.…”

Section: Numerical Examplementioning

confidence: 90%

Big in Japan: Regularizing Networks for Solving Inverse Problems

2019

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Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis for solving inverse problems by neural networks is mostly missing. In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form B + N @A B , where B is a classical regularization and the network N @A B is trained to recover the missing part Id X B not found by the classical regularization. We show that these regularizing networks yield a convergent regularization method for solving inverse problems. Additionally, we derive convergence rates (quantitative error estimates) assuming a sufficient decay of the associated distance function. We demonstrate that our results recover existing convergence and convergence rates results for filter-based regularization methods as well as the recently introduced null space network as special cases. Numerical results are presented for a tomographic sparse data problem, which clearly demonstrate that the proposed RegNets improve the classical regularization as well as the null space network.In this paper, we go one step further and generalize the concept of deep null space learning by allowing the network to also act in the orthogonal complement of the null space of A in a controlled manner. This is in particular useful if the operator contains several small singular values that are not strictly equal to zero. Similar to the components in the kernel, these parts are difficult to be reconstructed by a classical linear regularization method and quantitative error estimates require strong smoothness assumptions on the objects to be recovered. Learning almost invisible components can significantly improve reconstruction results for less smooth objects.

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Section: Numerical Examplementioning

confidence: 90%

Big in Japan: Regularizing Networks for Solving Inverse Problems

2019

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“…149 The strength of this approach is in the emphasis on the model in the data consistency term and convergence guarantees under certain conditions, 148 but time consuming iterative minimization with the explicit forward and adjoint models is still needed, similar to the learned gradient schemes. Another possibility for an augmented analytical approach is presented by Schwab et al, 150 who consider a data-driven extension of the truncated singular value decomposition, where the network is trained to produce the singular vectors corresponding to small singular values to improve reconstruction quality.…”

Section: Augmented Analytical Approachesmentioning

confidence: 99%

Deep learning in photoacoustic tomography: current approaches and future directions

2020

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Biomedical photoacoustic tomography, which can provide high-resolution 3D soft tissue images based on optical absorption, has advanced to the stage at which translation from the laboratory to clinical settings is becoming possible. The need for rapid image formation and the practical restrictions on data acquisition that arise from the constraints of a clinical workflow are presenting new image reconstruction challenges. There are many classical approaches to image reconstruction, but ameliorating the effects of incomplete or imperfect data through the incorporation of accurate priors is challenging and leads to slow algorithms. Recently, the application of deep learning (DL), or deep neural networks, to this problem has received a great deal of attention. We review the literature on learned image reconstruction, summarizing the current trends and explain how these approaches fit within, and to some extent have arisen from, a framework that encompasses classical reconstruction methods. In particular, it shows how these techniques can be understood from a Bayesian perspective, providing useful insights. We also provide a concise tutorial demonstration of three prototypical approaches to learned image reconstruction. The code and data sets for these demonstrations are available to researchers. It is anticipated that it is in in vivo applications-where data may be sparse, fast imaging critical, and priors difficult to construct by hand-that DL will have the most impact. With this in mind, we conclude with some indications of possible future research directions. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…49 Similarly, a deep CNN has been applied to the truncated singular-value-decomposition (SVD) of reconstructed images, in order to resolve the limited-view issue. 50 The performance of these early methods has yet to be tested on in vivo data. A novel approach by Zhang et al, known as Dual Domain U-net (DuDoUnet), utilizes input information from both the time domain and frequency domain in the form of DAS image and k-space image inputs, respectively (unreviewed preprint, URL: https://arxiv.org/abs/ 2011.06147).…”

Section: For Pre-processing Channel Datamentioning

confidence: 99%

Sounding out the hidden data: A concise review of deep learning in photoacoustic imaging

DiSpirito

Pramanik

et al. 2021

Exp Biol Med (Maywood)

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The rapidly evolving field of photoacoustic tomography utilizes endogenous chromophores to extract both functional and structural information from deep within tissues. It is this power to perform precise quantitative measurements in vivo—with endogenous or exogenous contrast —that makes photoacoustic tomography highly promising for clinical translation in functional brain imaging, early cancer detection, real-time surgical guidance, and the visualization of dynamic drug responses. Considering photoacoustic tomography has benefited from numerous engineering innovations, it is of no surprise that many of photoacoustic tomography’s current cutting-edge developments incorporate advances from the equally novel field of artificial intelligence. More specifically, alongside the growth and prevalence of graphical processing unit capabilities within recent years has emerged an offshoot of artificial intelligence known as deep learning. Rooted in the solid foundation of signal processing, deep learning typically utilizes a method of optimization known as gradient descent to minimize a loss function and update model parameters. There are already a number of innovative efforts in photoacoustic tomography utilizing deep learning techniques for a variety of purposes, including resolution enhancement, reconstruction artifact removal, undersampling correction, and improved quantification. Most of these efforts have proven to be highly promising in addressing long-standing technical obstacles where traditional solutions either completely fail or make only incremental progress. This concise review focuses on the history of applied artificial intelligence in photoacoustic tomography, presents recent advances at this multifaceted intersection of fields, and outlines the most exciting advances that will likely propagate into promising future innovations.

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Deep Learning of truncated singular values for limited view photoacoustic tomography

Cited by 16 publications

References 35 publications

Big in Japan: Regularizing Networks for Solving Inverse Problems

Big in Japan: Regularizing Networks for Solving Inverse Problems

Deep learning in photoacoustic tomography: current approaches and future directions

Sounding out the hidden data: A concise review of deep learning in photoacoustic imaging

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