In the past few years, group-based sparse representation (GSR) has emerged as a powerful paradigm for image inverse problems by synergizing model-driven interpretability with nonlocal self-similarity priors. Nevertheless, its practical utility is hindered by computationally expensive iterative processes. Deep learning (DL) methods can avoid this deficiency, but they often lack of model interpretability. To bridge this gap, we propose a novel deep group-based sparse representation framework, termed DeepGSR, which brings the GSR method and the DL approach together. DeepGSR not only circumvents the iterative bottlenecks of conventional GSR but also preserves its model interpretability through a learnable parameterization. Specifically, the network is built upon a GSR model that leverages nonlocal self-similarity, and it integrates adaptive patch matching and aggregation mechanisms to model complex intra-group relationships in the latent space. To reduce the computational complexity associated with traditional SVD-based rank shrinkage, we introduce a learnable low-rank shrinkage module that incorporates low-rank constraints while enhancing the interpretability and adaptability of the model. To better exploit frequency-specific structures, the network incorporates a shifting wavelet-domain patch partitioning strategy, which separately models high- and low-frequency components to further enhance the representation ability of the network. Extensive experiments demonstrate that DeepGSR, when applied as a drop-in replacement module to various image inverse problems such as image denoising, single-image deraining, metal artifact reduction, sparse-view computed tomography reconstruction, phase retrieval, and all-in-one image restoration consistently delivers effective performance, validating the effectiveness of the proposed framework. The source code and datasets have been made publicly available at https://github.com/shibaoshun/DeepGSR.

Despite significant advancements in deep learning-based sparse-view computed tomography (SVCT) reconstruction algorithms, these methods still encounter two primary limitations: (I) It is challenging to explicitly prove that the prior networks of deep unfolding algorithms satisfy Lipschitz constraints due to their empirically designed nature. (II) The substantial storage costs of training a separate model for each setting in the case of multiple views hinder practical clinical applications. To address these issues, we elaborate an explicitly provable Lipschitz-constrained network, dubbed LipNet, and integrate an explicit prompt module to provide discriminative knowledge of different sparse sampling settings, enabling the treatment of multiple sparse view configurations within a single model. Furthermore, we develop a storage-saving deep unfolding framework for multiple-in-one SVCT reconstruction, termed PromptCT, which embeds LipNet as its prior network to ensure the convergence of its corresponding iterative algorithm. In simulated and real data experiments, PromptCT outperforms benchmark reconstruction algorithms in multiple-in-one SVCT reconstruction, achieving higher-quality reconstructions with lower storage costs. On the theoretical side, we explicitly demonstrate that LipNet satisfies boundary property, further proving its Lipschitz continuity and subsequently analyzing the convergence of the proposed iterative algorithms. The data and code are publicly available at https://github.com/shibaoshun/PromptCT.

Compressive imaging (CI) aims to recover the underlying image from the under-sampled observations. Recently, deep unfolded CI (DUCI) algorithms, which unfold the iterative algorithms into deep neural networks (DNNs), have achieved remarkable results. Theoretically, unfolding a convergent iterative algorithm could ensure a stable DUCI algorithm, i.e., its performance increases as the increasing stage. However, ensuring convergence often involves imposing constraints, such as bounded spectral norm or tight property, on the filter weights or sparsifying transform. Unfortunately, these constraints may compromise algorithm performance. To address this challenge, we present a provably bounded dynamic sparsifying transform network (BSTNet), which can be explicitly proven to be a bounded network without imposing constraints on the analysis sparsifying transform. Leveraging this advantage, the analysis sparsifying transform can be adaptively generated via a trainable DNN. Specifically, we elaborate a dynamic sparsifying transform generator capable of extracting multiple feature information from input instances, facilitating the creation of a faithful content-adaptive sparsifying transform. We explicitly demonstrate that the proposed BSTNet is a bounded network, and further embed it as the prior network into a DUCI framework to evaluate its performance on two CI tasks, i.e., spectral snapshot CI (SCI) and compressed sensing magnetic resonance imaging (CSMRI). Experimental results showcase that our DUCI algorithms can achieve competitive recovery quality compared to benchmark algorithms. Theoretically, we explicitly prove that the proposed BSTNet is bounded, and we provide a comprehensive theoretical convergence analysis of the proposed iteration algorithms.

Video snapshot compressive imaging (SCI) is a new compressive imaging system that aims to recover multiple video frames from a single measurement. Recent plug-and-play (PnP) imaging methods have been used for solving SCI inverse problems by leveraging pre-trained deep Gaussian denoisers. Under the condition of diminishing noise levels , a necessary assumption for the fixed-point convergence of PnP imaging algorithms is that the plugged denoisers are bounded denoisers. However, it is difficult to prove that existing deep Gaussian denoisers meet this assumption due to the complex network architectures, limiting the convergence analysis of these algorithms. This paper aims to elaborate a bounded deep video denoiser to remedy such a gap. Concretely, we propose a denoiser using double tight frames dubbed as VDTF and plug it into the PnP framework to construct the PnP-VDTF algorithm. In VDTF, a constant network (CNet) is designed, wherein a Swin Transformer-based module and a 3D convolution module extract the spatial information of the global features and the temporal information of the input video, respectively. Theoretically, we provide a strict boundary proof of VDTF, and show that PnP-VDTF can generate fixed-point convergent trajectories. Experiments show that PnP-VDTF can achieve higher-quality reconstructions compared with benchmark SCI algorithms.

Due to the presence of metallic implants, the imaging quality of computed tomography (CT) is degraded by metal artifacts. Existing deep learning-based metal artifact reduction (MAR) methods focus on working locally within artifact and non-artifact regions, limiting in improving the performance of MAR, especially for large metal artifacts. To tackle the bottleneck, we propose a novel artifact region-aware transformer-based MAR network, dubbed MARFormer, which leverages non-artifact regions to aid in artifact region restoration. Specifically, we build an artifact mask estimation subnetwork to approximately identify artifact regions, while elaborate a local-global information interaction subnetwork consisting of a local information extraction module, an artifact region-aware attention module, and a channel attention fusion module (CAFM) to integrate local and global information. Under the guidance of the estimated artifact region, the proposed artifact region-aware attention module can effectively model the global context correlation between artifact and non-artifact regions. Additionally, the local and global information are adaptively fused using CAFM. Extensive experiments demonstrate that the proposed method outperforms the state-of-the-art MAR methods in terms of artifact reduction accuracy.

Recently, the PnP-GAP algorithm has achieved remarkable reconstruction quality for snapshot compressive imaging (SCI), and its convergence has been proven based on the condition of diminishing noise levels and the assumption of bounded denoisers. However, most of deep denoisers are difficult to be proven as bounded denoisers due to the lack of interpretability of deep network architectures. To address this issue, a trainable bounded denoiser using double tight frame network for SCI is proposed. Firstly, to achieve higher denoising ability, we extend the single-layer tight frame to the two-layer one dubbed as double tight frame. Then, we elaborate a deep shrinkage network (DSN) for improving the generalization ability of the plugged deep denoiser to noise levels. Finally, we employ the double tight frame equipped with DSN to construct a Gaussian denoiser that can be trained in a supervised learning manner. We prove this trainable denoiser is bounded theoretically, and demonstrate that the PnP-GAP framework plugged by this denoiser can achieve competitive reconstruction quality compared with benchmark SCI algorithms empirically.

Recovering the image of interest from its phaseless measurement is the goal of phase retrieval (PR). Recent PR algorithms that use hand-crafted priors suffer from low-quality reconstructions. To cope with this limitation, we exploit structural priors to propose a novel deep unfolded convolutional sparse coding phase retrieval network. Firstly, we formulate a weighted ℓ1norm (WL1) minimization problem utilizing convolutional sparse coding for PR, and solve it by using an iterative algorithm. An inertial epigraph method employing the inertial technique is proposed to solve the PR subproblem. Secondly, differing from updating weights of WL1 by using a fixed inverse proportional function in traditional methods, we learn such a function that can determine these crucial weights via a deep convolutional neural network equipped with the attention mechanism. Finally, we unroll the iterative PR algorithm to build a deep feedforward network architecture. Experiments demonstrate that the resulting model-based deep network can recover higherquality images, compared with the existing PR algorithms at various noise levels. The testing data and codes are published at https://github.com/shibaoshun/PRNet.

Abstract Data‐driven tight frames are popular for solving imaging inverse problems. However, the imaging quality is limited by the representation ability of single tight frame and thresholds tuned manually. In this work, a supervised dual tight frame learning framework fused with an elaborated deep thresholding network (DTN) is proposed, and the issue of low‐quality reconstructions in previous phase retrieval (PR) algorithms is addressed. To effectively learn dual tight frames, a loss function is formed using the mean square error, tight constraint, dual constraint, and sparse constraint terms. Moreover, to determine the thresholds adaptively, the thresholds are extracted from the frame coefficients via DTN. By an end‐to‐end supervised learning manner, the dual tight frames and DTN are jointly trained from labels and their counterparts corrupted by Gaussian noise. Using the Gaussian denoiser constructed by dual tight frames, a regularisation model is firstly designed, and then exploited to formulate a PR optimisation problem. The image filtering and image updating steps are performed alternatively for solving this problem. Particularly, the image updating subproblem is tackled by an inertial epigraph solver. The simulation experiments show that the proposed PR algorithm can obtain higher‐quality reconstructions compared with the benchmark ones.

Phase retrieval (PR), i.e., the recovery of the underlying image from the measurements without phase information, is a challenging task, especially at low signal to noise ratios (SNRs). Recent deep unrolling optimizations of tackling this task offer both computational efficiency and high-quality reconstructions. In this work, we involve a novel deep shrinkage network (DSN) into the supervised dual frame learning framework, and propose a deep shrinkage dual frame network dubbed as DualNet for building a deep unrolled PR network architecture. Traditional thresholding functions with hand-crafted thresholds for filtering the frame coefficients are non-adaptive, which limits the final reconstruction quality. Instead, we elaborate a DSN that can learn instance-adaptive and spatial-variant thresholding functions. In a nutshell, we propose the so-called DualPRNet by incorporating the learned dual frames into the unrolled PR framework. Experiments demonstrate that DualPRNet can achieve higher-quality reconstructions compared with previous PR iteration algorithms at low SNRs.

The signal degradation due to the Poisson noise is a common problem in the low‐light imaging field. Recently, deep learning employing the convolution neural network for image denoising has drawn considerable attention owing to its favourable denoising performance. On the basis of the fact that the reconstruction of corrupted pixels can be facilitated by the context information in image denoising, the authors propose a deep multi‐scale cross‐path concatenation residual network (MC 2 RNet) which incorporates cross‐path concatenation modules for Poisson denoising. Multiple paths are achieved by the cross‐path concatenation operation and the skip connection. As a consequence, multi‐scale context representations of images under different receptive fields can be learnt by MC 2 RNet. With the residual learning strategy, MC 2 RNet learns the residual between the noisy image and the latent clean image rather than the direct mapping to facilitate model training. Specially, unlike existing discriminative Poisson denoising algorithms that train a model only for the specific noise level, they aim to train a single model for handling Poisson noise with different levels, i.e. blind Poisson denoising. Quantitative experiments demonstrate that the proposed model is superior over the state‐of‐the‐art Poisson denoising approaches in terms of peak signal‐to‐noise ratio and visual effect.

Compressed sensing (CS) enables that magnetic resonance (MR) images can be exactly reconstructed from undersampled k ‐space data by exploiting the sparsity of MR images in some analytical sparsifying transform or some dictionary. Recent methods are exploiting adaptive patch‐based dictionaries for image recovery by alternating between dictionary learning step and image reconstruction step. In this study, the authors propose a novel MR image reconstruction algorithm utilising dictionary updating, which consists of three steps: sparse coding, dictionary updating and image reconstruction. In the dictionary updating step, they perform a first‐order series expansion for dictionary–coefficient matrix product via recursive method, and propose an efficient method to solve the new dictionary updating problem. To improve the reconstruction quality, the proposed block‐matching and three‐dimensional (3D) filtering regularisation is incorporated into the authors’ image CS recovery, which can combine the self‐similarities within the image, the 3D transform sparsity and the local sparsity into image recovery process. Experimental simulations demonstrate their proposed algorithms can obtain better reconstruction quality than the previous CS algorithms.