Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift. To address these shortcomings, we build interpretable networks by unrolling variants of a graph-based optimization algorithm of different complexities. Specifically, for a general linear image formation model, we first formulate a convex quadratic programming (QP) problem with a new $\ell_2$-norm graph smoothness prior called gradient graph Laplacian regularizer (GGLR) that promotes piecewise planar (PWP) signal reconstruction. To solve the posed unconstrained QP problem, instead of computing a linear system solution straightforwardly, we introduce a variable number of auxiliary variables and correspondingly design a family of ADMM algorithms. We then unroll them into variable-complexity feed-forward networks, amenable to parameter tuning via back-propagation. More complex unrolled networks require more labeled data to train more parameters, but have better overall performance. The unrolled networks have periodic insertions of a graph learning module, akin to a self-attention mechanism in a transformer architecture, to learn pairwise similarity structure inherent in data. Experimental results show that our unrolled networks perform competitively to generic DL networks in image restoration quality while using only a fraction of parameters, and demonstrate improved robustness to covariate shift.
Image deblurring in photon-limited conditions is ubiquitous in a variety of low-light applications such as photography, microscopy, and astronomy. However, the presence of photon shot noise due to low illumination and/or short exposure makes the deblurring task substantially more challenging than the conventional deblurring problems. In this paper, we present an algorithm unrolling approach for the photon-limited deblurring problem by unrolling a Plug-and-Play algorithm for a fixed number of iterations. By introducing a three-operator splitting formation of the Plug-and-Play framework, we obta…
A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution
Department of Computer Engineering and Informatics, Patras University（计算机工程与信息学院，帕特拉大学）；Department Digital Media and Communication, Ionian University（数字媒体与通信系，伊奥尼亚大学）
In inverse problems we aim to reconstruct some underlying signal of interest from potentially corrupted and often ill-posed measurements. Classical optimization-based techniques proceed by optimizing a data consistency metric together with a regularizer. Current state-of-the-art machine learning approaches draw inspiration from such techniques by unrolling the iterative updates for an optimization-based solver and then learning a regularizer from data. This loop unrolling (LU) method has shown tremendous success, but often requires a deep model for the best performance leading to high memory c…
There has been tremendous research on the design of image regularizers over the years, from simple Tikhonov and Laplacian to sophisticated sparsity and CNN-based regularizers. Coupled with a model-based loss function, these are typically used for image reconstruction within an optimization framework. The technical challenge is to develop a regularizer that can accurately model realistic images and be optimized efficiently along with the loss function. Motivated by the recent plug-and-play paradigm for image regularization, we construct a quadratic regularizer whose reconstruction capability is…
In plug-and-play (PnP) regularization, the knowledge of the forward model is combined with a powerful denoiser to obtain state-of-the-art image reconstructions. This is typically done by taking a proximal algorithm such as FISTA or ADMM, and formally replacing the proximal map associated with a regularizer by nonlocal means, BM3D or a CNN denoiser. Each iterate of the resulting PnP algorithm involves some kind of inversion of the forward model followed by denoiser-induced regularization. A natural question in this regard is that of optimality, namely, do the PnP iterations minimize some f+g, w…
There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the development of fast algorithms for solving the dictionary learning and sparse coding problems for sufficiently large images and data sets. Nevertheless, this model has seen very limited application to tomographic reconstruction problems. In this paper, we present a model-based tomographic reconstruction algorithm using a learnt convolutional dictionary as a reg…
Existing physical model-based imaging methods for ultrasound elasticity reconstruction utilize fixed variational regularizers that may not be appropriate for the application of interest or may not capture complex spatial prior information about the underlying tissues. On the other hand, end-to-end learning-based methods count solely on the training data, not taking advantage of the governing physical laws of the imaging system. Integrating learning-based priors with physical forward models for ultrasound elasticity imaging, we present a joint reconstruction framework which guarantees that lear…
The Plug-and-Play (PnP) framework makes it possible to integrate advanced image denoising priors into optimization algorithms, to efficiently solve a variety of image restoration tasks generally formulated as Maximum A Posteriori (MAP) estimation problems. The Plug-and-Play alternating direction method of multipliers (ADMM) and the Regularization by Denoising (RED) algorithms are two examples of such methods that made a breakthrough in image restoration. However, while the former method only applies to proximal algorithms, it has recently been shown that there exists no regularization that exp…
Spectral unmixing is a widely used technique in hyperspectral image processing and analysis. It aims to separate mixed pixels into the component materials and their corresponding abundances. Early solutions to spectral unmixing are performed independently on each pixel. Nowadays, investigating proper priors into the unmixing problem has been popular as it can significantly enhance the unmixing performance. However, it is non-trivial to handcraft a powerful regularizer, and complex regularizers may introduce extra difficulties in solving optimization problems in which they are involved. To addr…
Plug-and-Play Priors (PnP) is one of the most widely-used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods for prior modeling of data to provide state-of-the-art reconstruction algorithms. PnP algorithms alternate between minimizing a data-fidelity term to promote data consistency and imposing a learned regularizer in the form of an image denoiser. Recent highly-successful applications of PnP algorithms include bio-microscopy, computerized…
In Plug-and-Play (PnP) algorithms, an off-the-shelf denoiser is used for image regularization. PnP yields state-of-the-art results, but its theoretical aspects are not well understood. This work considers the question: Similar to classical compressed sensing (CS), can we theoretically recover the ground-truth via PnP under suitable conditions on the denoiser and the sensing matrix? One hurdle is that since PnP is an algorithmic framework, its solution need not be the minimizer of some objective function. It was recently shown that a convex regularizer $Φ$ can be associated with a class of line…
School of Marine Science and Technology, Northwestern Polytechnical University, China（西北工业大学海洋科学与技术学院）；State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, China（北京交通大学轨道交通控制与安全国家重点实验室）
Nowadays, nonnegative matrix factorization (NMF) based methods have been widely applied to blind spectral unmixing. Introducing proper regularizers to NMF is crucial for mathematically constraining the solutions and physically exploiting spectral and spatial properties of images. Generally, properly handcrafting regularizers and solving the associated complex optimization problem are non-trivial tasks. In our work, we propose an NMF based unmixing framework which jointly uses a handcrafting regularizer and a learnt regularizer from data. we plug learnt priors of abundances where the associated…
A standard model for image reconstruction involves the minimization of a data-fidelity term along with a regularizer, where the optimization is performed using proximal algorithms such as ISTA and ADMM. In plug-and-play (PnP) regularization, the proximal operator (associated with the regularizer) in ISTA and ADMM is replaced by a powerful image denoiser. Although PnP regularization works surprisingly well in practice, its theoretical convergence -- whether convergence of the PnP iterates is guaranteed and if they minimize some objective function -- is not completely understood even for simple …
SIAT（中国科学院深圳先进技术研究院）；National Innovation Center for Advanced Medical Devices（国家高性能医疗器械创新中心）；Shanghai Jiaotong University（上海交通大学）；Technical University of Munich（慕尼黑工业大学）
Recently, model-driven deep learning unrolls a certain iterative algorithm of a regularization model into a cascade network by replacing the first-order information (i.e., (sub)gradient or proximal operator) of the regularizer with a network module, which appears more explainable and predictable compared to common data-driven networks. Conversely, in theory, there is not necessarily such a functional regularizer whose first-order information matches the replaced network module, which means the network output may not be covered by the original regularization model. Moreover, up to now, there is…
Plug-and-play (PnP) method is a recent paradigm for image regularization, where the proximal operator (associated with some given regularizer) in an iterative algorithm is replaced with a powerful denoiser. Algorithmically, this involves repeated inversion (of the forward model) and denoising until convergence. Remarkably, PnP regularization produces promising results for several restoration applications. However, a fundamental question in this regard is the theoretical convergence of the PnP iterations, since the algorithm is not strictly derived from an optimization framework. This question …
Harvard Medical School（哈佛医学院）；Boston Children’s Hospital（波士顿儿童医院）
Fast data acquisition in Magnetic Resonance Imaging (MRI) is vastly in demand and scan time directly depends on the number of acquired k-space samples. Conventional MRI reconstruction methods for fast MRI acquisition mostly relied on different regularizers which represent analytical models of sparsity. However, recent data-driven methods based on deep learning has resulted in promising improvements in image reconstruction algorithms. In this paper, we propose a deep plug-and-play prior framework for parallel MRI reconstruction problems which utilize a deep neural network (DNN) as an advanced d…
City University of Hong Kong（香港城市大学）；The Chinese University of Hong Kong（香港中文大学）；Hong Kong Centre for Cerebro-Cardiovascular Health Engineering（香港脑心血管健康工程中心）；University of Hong Kong（香港大学）
Spherical image processing has been widely applied in many important fields, such as omnidirectional vision for autonomous cars, global climate modelling, and medical imaging. It is non-trivial to extend an algorithm developed for flat images to the spherical ones. In this work, we focus on the challenging task of spherical image inpainting with deep learning-based regularizer. Instead of a naive application of existing models for planar images, we employ a fast directional spherical Haar framelet transform and develop a novel optimization framework based on a sparsity assumption of the framel…
University of Electronic Science and Technology of China（电子科技大学）；Southwestern University of Finance and Economics（西南财经大学）；Xi’an Jiaotong University（西安交通大学）
Multi-dimensional images, such as color images and multi-spectral images, are highly correlated and contain abundant spatial and spectral information. However, real-world multi-dimensional images are usually corrupted by missing entries. By integrating deterministic low-rankness prior to the data-driven deep prior, we suggest a novel regularized tensor completion model for multi-dimensional image completion. In the objective function, we adopt the newly emerged tensor nuclear norm (TNN) to characterize the global low-rankness prior of the multi-dimensional images. We also formulate an implicit…
Northwestern Polytechnical University（西北工业大学）；Research and Development Institute of Northwestern Polytechnical University in Shenzhen（西北工业大学深圳研究院）；Xi’an Jiaotong University（西安交通大学）；ETH Zurich（苏黎世联邦理工学院）
Analysis and Synthesis Denoisers for Forward-Backward Plug-and-Play Algorithms
Laboratoire Interdisciplinaire des Sciences du Numériques, Inria, Université Paris-Saclay, CNRS, Gif-sur-Yvette, France（跨学科数字科学实验室，法国国家信息与自动化研究所，巴黎-萨克雷大学，法国国家科学研究中心，法国吉夫-sur-伊夫特）；Inria, Université Paris-Saclay, CEA, Palaiseau, France（法国国家信息与自动化研究所，巴黎-萨克雷大学，法国原子能委员会，法国帕莱索）；School of Mathematics and Computer Sciences and School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK（数学与计算机科学学院和工程与物理科学学院，赫里奥特-瓦特大学，英国爱丁堡）；Maxwell Institute for Mathematical Sciences, Edinburgh, UK（数学科学麦克斯韦研究所，英国爱丁堡）
Physics-guided deep learning (PG-DL) via algorithm unrolling has received significant interest for improved image reconstruction, including MRI applications. These methods unroll an iterative optimization algorithm into a series of regularizer and data consistency units. The unrolled networks are typically trained end-to-end using a supervised approach. Current supervised PG-DL approaches use all of the available sub-sampled measurements in their data consistency units. Thus, the network learns to fit the rest of the measurements. In this study, we propose to improve the performance and robust…
Purpose: The goal of this study is to develop a novel deep learning (DL) based reconstruction framework to improve the digital breast tomosynthesis (DBT) imaging performance. Methods: In this work, the DIR-DBTnet is developed for DBT image reconstruction by unrolling the standard iterative reconstruction algorithm within the deep learning framework. In particular, such network learns the regularizer and the iteration parameters automatically through network training with a large amount of simulated DBT data. Afterwards, both numerical and experimental data are used to evaluate its performance.…
A Convergent Generalized Krylov Subspace Method for Compressed Sensing MRI Reconstruction with Gradient-Driven Denoisers
Oden Institute for Computational Engineering and Sciences, University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学学院）；Department of Electrical and Computer Engineering, University of Michigan（密歇根大学电气与计算机工程系）
Dalian University of Technology（大连理工大学）；Hangzhou Dianzi University（杭州电子科技大学）；Guilin University of Electronic Technology（桂林电子科技大学）
Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR data acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse problem to reconstruct aliasing-free MR images from the sparse k-space data. Conventional methods typically optimize an energy function, producing reconstruction of high quality, but their iterative numerical solvers unavoidably bring extremely slow processing. Recent data-driven techniques are able to provide fast restoration by either learning direct prediction…
Unsupervised Deformable Image Registration with Structural Nonparametric Smoothing
Cornell University（康奈尔大学）；Hunan University（湖南大学）；University of Pennsylvania（宾夕法尼亚大学）；Johns Hopkins University（约翰霍普金斯大学）；Shanghai Jiao Tong University（上海交通大学）；University of Birmingham（伯明翰大学）；University of Manchester（曼彻斯特大学）
