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.
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.
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.
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.
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.
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.