Recently, Deep Unfolding Networks (DUNs) have achieved impressive reconstruction quality in the field of image Compressive Sensing (CS) by unfolding iterative optimization algorithms into neural networks. The reconstruction quality of DUNs depends on the learned prior knowledge, so introducing stronger prior knowledge can further improve reconstruction quality. On the other hand, pre-trained diffusion models contain powerful prior knowledge and have a solid theoretical foundation and strong scalability, but it requires a large number of iterative steps to achieve reconstruction. In this paper, we propose to use the powerful prior knowledge of pre-trained diffusion model in DUNs to achieve high-quality reconstruction with less steps for image CS. Specifically, we first design an iterative optimization algorithm named Diffusion Message Passing (DMP), which embeds a pre-trained diffusion model into each iteration process of DMP. Then, we deeply unfold the DMP algorithm into a neural network named DMP-DUN. The proposed DMP-DUN can use lightweight neural networks to achieve mapping from measurement data to the intermediate steps of the reverse diffusion process and directly approximate the divergence of the diffusion model, thereby further improving reconstruction efficiency. Extensive experiments show that our proposed DMP-DUN achieves state-of-the-art performance and requires at least only 2 steps to reconstruct the image. Codes are available at https://github.com/FengodChen/DMP-DUN-CVPR2025.
Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face the following issues: 1) they learn directly from single-channel images, leading to a simple feature representation that does not fully capture complex features; and 2) they treat various image components uniformly, ignoring the characteristics of different components. To address these issues, we propose a novel wavelet-domain deep unfolding framework named WTDUN, which operates directly on the multi-scale wavelet subbands. Our method utilizes the intrinsic sparsity and multi-scale structure of wavelet coefficients to achieve a tree-structured sampling and reconstruction, effectively capturing and highlighting the most important features within images. Specifically, the design of tree-structured reconstruction aims to capture the inter-dependencies among the multi-scale subbands, enabling the identification of both fine and coarse features, which can lead to a marked improvement in reconstruction quality. Furthermore, a wavelet domain adaptive sampling method is proposed to greatly improve the sampling capability, which is realized by assigning measurements to each wavelet subband based on its importance. Unlike pure deep learning methods that treat all components uniformly, our method introduces a targeted focus on important subbands, considering their energy and sparsity. This targeted strategy lets us capture key information more efficiently while discarding less important information, resulting in a more effective and detailed reconstruction. Extensive experimental results on various datasets validate the superior performance of our proposed method.
Low-rank regularization-based deep unrolling networks have achieved remarkable success in various inverse imaging problems (IIPs). However, the singular value decomposition (SVD) is non-differentiable when duplicated singular values occur, leading to severe numerical instability during training. In this paper, we propose a differentiable SVD based on the Moore-Penrose pseudoinverse to address this issue. To the best of our knowledge, this is the first work to provide a comprehensive analysis of the differentiability of the trivial SVD. Specifically, we show that the non-differentiability of SVD is essentially due to an underdetermined system of linear equations arising in the derivation process. We utilize the Moore-Penrose pseudoinverse to solve the system, thereby proposing a differentiable SVD. A numerical stability analysis in the context of IIPs is provided. Experimental results in color image compressed sensing and dynamic MRI reconstruction show that our proposed differentiable SVD can effectively address the numerical instability issue while ensuring computational precision. Code is available at https://github.com/yhao-z/SVD-inv.
While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment. Although recent methods utilize pre-trained diffusion models for image reconstruction, they struggle with slow inference and restricted adaptability to CS. To tackle these challenges, this paper proposes Invertible Diffusion Models (IDM), a novel efficient, end-to-end diffusion-based CS method. IDM repurposes a large-scale diffusion sampling process as a reconstruction model, and fine-tunes it end-to-end to recover original images directly from CS measurements, moving beyond the traditional paradigm of one-step noise estimation learning. To enable such memory-intensive end-to-end fine-tuning, we propose a novel two-level invertible design to transform both (1) multi-step sampling process and (2) noise estimation U-Net in each step into invertible networks. As a result, most intermediate features are cleared during training to reduce up to 93.8% GPU memory. In addition, we develop a set of lightweight modules to inject measurements into noise estimator to further facilitate reconstruction. Experiments demonstrate that IDM outperforms existing state-of-the-art CS networks by up to 2.64dB in PSNR. Compared to the recent diffusion-based approach DDNM, our IDM achieves up to 10.09dB PSNR gain and 14.54 times faster inference. Code is available at https://github.com/Guaishou74851/IDM.
Existing image compressed sensing (CS) coding frameworks usually solve an inverse problem based on measurement coding and optimization-based image reconstruction, which still exist the following two challenges: 1) The widely used random sampling matrix, such as the Gaussian Random Matrix (GRM), usually leads to low measurement coding efficiency. 2) The optimization-based reconstruction methods generally maintain a much higher computational complexity. In this paper, we propose a new CNN based image CS coding framework using local structural sampling (dubbed CSCNet) that includes three functional modules: local structural sampling, measurement coding and Laplacian pyramid reconstruction. In the proposed framework, instead of GRM, a new local structural sampling matrix is first developed, which is able to enhance the correlation between the measurements through a local perceptual sampling strategy. Besides, the designed local structural sampling matrix can be jointly optimized with the other functional modules during training process. After sampling, the measurements with high correlations are produced, which are then coded into final bitstreams by the third-party image codec. At last, a Laplacian pyramid reconstruction network is proposed to efficiently recover the target image from the measurement domain to the image domain. Extensive experimental results demonstrate that the proposed scheme outperforms the existing state-of-the-art CS coding methods, while maintaining fast computational speed.
Conventional compressed sensing (CS) algorithms typically apply a uniform sampling rate to different image blocks. A more strategic approach could be to allocate the number of measurements adaptively, based on each image block's complexity. In this paper, we propose a Measurement-Bounds-based Rate-Adaptive Image Compressed Sensing Network (MB-RACS) framework, which aims to adaptively determine the sampling rate for each image block in accordance with traditional measurement bounds theory. Moreover, since in real-world scenarios statistical information about the original image cannot be directly obtained, we suggest a multi-stage rate-adaptive sampling strategy. This strategy sequentially adjusts the sampling ratio allocation based on the information gathered from previous samplings. We formulate the multi-stage rate-adaptive sampling as a convex optimization problem and address it using a combination of Newton's method and binary search techniques. Additionally, we enhance our decoding process by incorporating skip connections between successive iterations to facilitate a richer transmission of feature information across iterations. Our experiments demonstrate that the proposed MB-RACS method surpasses current leading methods, with experimental evidence also underscoring the effectiveness of each module within our proposed framework.
Popular methods in compressed sensing (CS) are dependent on deep learning (DL), where large amounts of data are used to train non-linear reconstruction models. However, ensuring generalisability over and access to multiple datasets is challenging to realise for real-world applications. To address these concerns, this paper proposes a single image, self-supervised (SS) CS-MRI framework that enables a joint deep and sparse regularisation of CS artefacts. The approach effectively dampens structured CS artefacts, which can be difficult to remove assuming sparse reconstruction, or relying solely on the inductive biases of CNN to produce noise-free images. Image quality is thereby improved compared to either approach alone. Metrics are evaluated using Cartesian 1D masks on a brain and knee dataset, with PSNR improving by 2-4dB on average.
Inspired by certain optimization solvers, the deep unfolding network (DUN) has attracted much attention in recent years for image compressed sensing (CS). However, there still exist the following two issues: 1) In existing DUNs, most hyperparameters are usually content independent, which greatly limits their adaptability for different input contents. 2) In each iteration, a plain convolutional neural network is usually adopted, which weakens the perception of wider context prior and therefore depresses the expressive ability. In this paper, inspired by the traditional Proximal Gradient Descent (PGD) algorithm, a novel DUN for image compressed sensing (dubbed DUN-CSNet) is proposed to solve the above two issues. Specifically, for the first issue, a novel content adaptive gradient descent network is proposed, in which a well-designed step size generation sub-network is developed to dynamically allocate the corresponding step sizes for different textures of input image by generating a content-aware step size map, realizing a content-adaptive gradient updating. For the second issue, considering the fact that many similar patches exist in an image but have undergone a deformation, a novel deformation-invariant non-local proximal mapping network is developed, which can adaptively build the long-range dependencies between the nonlocal patches by deformation-invariant non-local modeling, leading to a wider perception on context priors. Extensive experiments manifest that the proposed DUN-CSNet outperforms existing state-of-the-art CS methods by large margins.
By absorbing the merits of both the model- and data-driven methods, deep physics-engaged learning scheme achieves high-accuracy and interpretable image reconstruction. It has attracted growing attention and become the mainstream for inverse imaging tasks. Focusing on the image compressed sensing (CS) problem, we find the intrinsic defect of this emerging paradigm, widely implemented by deep algorithm-unrolled networks, in which more plain iterations involving real physics will bring enormous computation cost and long inference time, hindering their practical application. A novel deep $\textbf{P}$hysics-guided un$\textbf{R}$olled recovery $\textbf{L}$earning ($\textbf{PRL}$) framework is proposed by generalizing the traditional iterative recovery model from image domain (ID) to the high-dimensional feature domain (FD). A compact multiscale unrolling architecture is then developed to enhance the network capacity and keep real-time inference speeds. Taking two different perspectives of optimization and range-nullspace decomposition, instead of building an algorithm-specific unrolled network, we provide two implementations: $\textbf{PRL-PGD}$ and $\textbf{PRL-RND}$. Experiments exhibit the significant performance and efficiency leading of PRL networks over other state-of-the-art methods with a large potential for further improvement and real application to other inverse imaging problems or optimization models.
Deep learning based image compressed sensing (CS) has achieved great success. However, existing CS systems mainly adopt a fixed measurement matrix to images, ignoring the fact the optimal measurement numbers and bases are different for different images. To further improve the sensing efficiency, we propose a novel semantic-aware image CS system. In our system, the encoder first uses a fixed number of base CS measurements to sense different images. According to the base CS results, the encoder then employs a policy network to analyze the semantic information in images and determines the measurement matrix for different image areas. At the decoder side, a semantic-aware initial reconstruction network is developed to deal with the changes of measurement matrices used at the encoder. A rate-distortion training loss is further introduced to dynamically adjust the average compression ratio for the semantic-aware CS system and the policy network is trained jointly with the encoder and the decoder in an en-to-end manner by using some proxy functions. Numerical results show that the proposed semantic-aware image CS system is superior to the traditional ones with fixed measurement matrices.
The learned denoising-based approximate message passing (LDAMP) algorithm has attracted great attention for image compressed sensing (CS) tasks. However, it has two issues: first, its global measurement model severely restricts its applicability to high-dimensional images, and its block-based measurement method exhibits obvious block artifacts; second, the denoiser in the LDAMP is too simple, and existing denoisers have limited ability in detail recovery. In this paper, to overcome the issues and develop a high-performance LDAMP method for image block compressed sensing (BCS), we propose a novel sparsity and coefficient permutation-based AMP (SCP-AMP) method consisting of the block-based sampling and the two-domain reconstruction modules. In the sampling module, SCP-AMP adopts a discrete cosine transform (DCT) based sparsity strategy to reduce the impact of the high-frequency coefficient on the reconstruction, followed by a coefficient permutation strategy to avoid block artifacts. In the reconstruction module, a two-domain AMP method with DCT domain noise correction and pixel domain denoising is proposed for iterative reconstruction. Regarding the denoiser, we proposed a multi-level deep attention network (MDANet) to enhance the texture details by employing multi-level features and multiple attention mechanisms. Extensive experiments demonstrated that the proposed SCP-AMP method achieved better reconstruction accuracy than other state-of-the-art BCS algorithms in terms of both visual perception and objective metrics.
Most existing Image Restoration (IR) models are task-specific, which can not be generalized to different degradation operators. In this work, we propose the Denoising Diffusion Null-Space Model (DDNM), a novel zero-shot framework for arbitrary linear IR problems, including but not limited to image super-resolution, colorization, inpainting, compressed sensing, and deblurring. DDNM only needs a pre-trained off-the-shelf diffusion model as the generative prior, without any extra training or network modifications. By refining only the null-space contents during the reverse diffusion process, we can yield diverse results satisfying both data consistency and realness. We further propose an enhanced and robust version, dubbed DDNM+, to support noisy restoration and improve restoration quality for hard tasks. Our experiments on several IR tasks reveal that DDNM outperforms other state-of-the-art zero-shot IR methods. We also demonstrate that DDNM+ can solve complex real-world applications, e.g., old photo restoration.
Most Deep Learning (DL) based Compressed Sensing (DCS) algorithms adopt a single neural network for signal reconstruction, and fail to jointly consider the influences of the sampling operation for reconstruction. In this paper, we propose unified framework, which jointly considers the sampling and reconstruction process for image compressive sensing based on well-designed cascade neural networks. Two sub-networks, which are the sampling sub-network and the reconstruction sub-network, are included in the proposed framework. In the sampling sub-network, an adaptive full connected layer instead of the traditional random matrix is used to mimic the sampling operator. In the reconstruction sub-network, a cascade network combining stacked denoising autoencoder (SDA) and convolutional neural network (CNN) is designed to reconstruct signals. The SDA is used to solve the signal mapping problem and the signals are initially reconstructed. Furthermore, CNN is used to fully recover the structure and texture features of the image to obtain better reconstruction performance. Extensive experiments show that this framework outperforms many other state-of-the-art methods, especially at low sampling rates.
Deep Learning (DL) based Compressed Sensing (CS) has been applied for better performance of image reconstruction than traditional CS methods. However, most existing DL methods utilize the block-by-block measurement and each measurement block is restored separately, which introduces harmful blocking effects for reconstruction. Furthermore, the neuronal receptive fields of those methods are designed to be the same size in each layer, which can only collect single-scale spatial information and has a negative impact on the reconstruction process. This paper proposes a novel framework named Multi-scale Dilated Convolution Neural Network (MsDCNN) for CS measurement and reconstruction. During the measurement period, we directly obtain all measurements from a trained measurement network, which employs fully convolutional structures and is jointly trained with the reconstruction network from the input image. It needn't be cut into blocks, which effectively avoids the block effect. During the reconstruction period, we propose the Multi-scale Feature Extraction (MFE) architecture to imitate the human visual system to capture multi-scale features from the same feature map, which enhances the image feature extraction ability of the framework and improves the performance of image reconstruction. In the MFE, there are multiple parallel convolution channels to obtain multi-scale feature information. Then the multi-scale features information is fused and the original image is reconstructed with high quality. Our experimental results show that the proposed method performs favorably against the state-of-the-art methods in terms of PSNR and SSIM.
By integrating certain optimization solvers with deep neural network, deep unfolding network (DUN) has attracted much attention in recent years for image compressed sensing (CS). However, there still exist several issues in existing DUNs: 1) For each iteration, a simple stacked convolutional network is usually adopted, which apparently limits the expressiveness of these models. 2) Once the training is completed, most hyperparameters of existing DUNs are fixed for any input content, which significantly weakens their adaptability. In this paper, by unfolding the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), a novel fast hierarchical DUN, dubbed FHDUN, is proposed for image compressed sensing, in which a well-designed hierarchical unfolding architecture is developed to cooperatively explore richer contextual prior information in multi-scale spaces. To further enhance the adaptability, series of hyperparametric generation networks are developed in our framework to dynamically produce the corresponding optimal hyperparameters according to the input content. Furthermore, due to the accelerated policy in FISTA, the newly embedded acceleration module makes the proposed FHDUN save more than 50% of the iterative loops against recent DUNs. Extensive CS experiments manifest that the proposed FHDUN outperforms existing state-of-the-art CS methods, while maintaining fewer iterations.
To more efficiently address image compressed sensing (CS) problems, we present a novel content-aware scalable network dubbed CASNet which collectively achieves adaptive sampling rate allocation, fine granular scalability and high-quality reconstruction. We first adopt a data-driven saliency detector to evaluate the importances of different image regions and propose a saliency-based block ratio aggregation (BRA) strategy for sampling rate allocation. A unified learnable generating matrix is then developed to produce sampling matrix of any CS ratio with an ordered structure. Being equipped with the optimization-inspired recovery subnet guided by saliency information and a multi-block training scheme preventing blocking artifacts, CASNet jointly reconstructs the image blocks sampled at various sampling rates with one single model. To accelerate training convergence and improve network robustness, we propose an SVD-based initialization scheme and a random transformation enhancement (RTE) strategy, which are extensible without introducing extra parameters. All the CASNet components can be combined and learned end-to-end. We further provide a four-stage implementation for evaluation and practical deployments. Experiments demonstrate that CASNet outperforms other CS networks by a large margin, validating the collaboration and mutual supports among its components and strategies. Codes are available at https://github.com/Guaishou74851/CASNet.
Recently, deep network-based image compressed sensing methods achieved high reconstruction quality and reduced computational overhead compared with traditional methods. However, existing methods obtain measurements only from partial features in the network and use them only once for image reconstruction. They ignore there are low, mid, and high-level features in the network\cite{zeiler2014visualizing} and all of them are essential for high-quality reconstruction. Moreover, using measurements only once may not be enough for extracting richer information from measurements. To address these issues, we propose a novel Measurements Reuse Convolutional Compressed Sensing Network (MR-CCSNet) which employs Global Sensing Module (GSM) to collect all level features for achieving an efficient sensing and Measurements Reuse Block (MRB) to reuse measurements multiple times on multi-scale. Finally, experimental results on three benchmark datasets show that our model can significantly outperform state-of-the-art methods.
Deep network-based image Compressed Sensing (CS) has attracted much attention in recent years. However, the existing deep network-based CS schemes either reconstruct the target image in a block-by-block manner that leads to serious block artifacts or train the deep network as a black box that brings about limited insights of image prior knowledge. In this paper, a novel image CS framework using non-local neural network (NL-CSNet) is proposed, which utilizes the non-local self-similarity priors with deep network to improve the reconstruction quality. In the proposed NL-CSNet, two non-local subnetworks are constructed for utilizing the non-local self-similarity priors in the measurement domain and the multi-scale feature domain respectively. Specifically, in the subnetwork of measurement domain, the long-distance dependencies between the measurements of different image blocks are established for better initial reconstruction. Analogically, in the subnetwork of multi-scale feature domain, the affinities between the dense feature representations are explored in the multi-scale space for deep reconstruction. Furthermore, a novel loss function is developed to enhance the coupling between the non-local representations, which also enables an end-to-end training of NL-CSNet. Extensive experiments manifest that NL-CSNet outperforms existing state-of-the-art CS methods, while maintaining fast computational speed.
In this paper, we reformulate the non-convex $\ell_q$-norm minimization problem with $q\in(0,1)$ into a 2-step problem, which consists of one convex and one non-convex subproblems, and propose a novel iterative algorithm called QISTA ($\ell_q$-ISTA) to solve the $\left(\ell_q\right)$-problem. By taking advantage of deep learning in accelerating optimization algorithms, together with the speedup strategy that using the momentum from all previous layers in the network, we propose a learning-based method, called QISTA-Net-s, to solve the sparse signal reconstruction problem. Extensive experimental comparisons demonstrate that the QISTA-Net-s yield better reconstruction qualities than state-of-the-art $\ell_1$-norm optimization (plus learning) algorithms even if the original sparse signal is noisy. On the other hand, based on the network architecture associated with QISTA, with considering the use of convolution layers, we proposed the QISTA-Net-n for solving the image CS problem, and the performance of the reconstruction still outperforms most of the state-of-the-art natural images reconstruction methods. QISTA-Net-n is designed in unfolding QISTA and adding the convolutional operator as the dictionary. This makes QISTA-Net-s interpretable. We provide complete experimental results that QISTA-Net-s and QISTA-Net-n contribute the better reconstruction performance than the competing.
Group sparse representation (GSR) based method has led to great successes in various image recovery tasks, which can be converted into a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually leads to over-shrinking problem, since the standard soft-thresholding operator shrinks all singular values equally. To improve traditional sparse representation based image compressive sensing (CS) performance, we propose a generalized CS framework based on GSR model, which leads to a nonconvex nonsmooth low-rank minimization problem. The popular L_2-norm and M-estimator are employed for standard image CS and robust CS problem to fit the data respectively. For the better approximation of the rank of group-matrix, a family of nuclear norms are employed to address the over-shrinking problem. Moreover, we also propose a flexible and effective iteratively-weighting strategy to control the weighting and contribution of each singular value. Then we develop an iteratively reweighted nuclear norm algorithm for our generalized framework via an alternating direction method of multipliers framework, namely, GSR-AIR. Experimental results demonstrate that our proposed CS framework can achieve favorable reconstruction performance compared with current state-of-the-art methods and the robust CS framework can suppress the outliers effectively.