Sparse representation via dedicated dictionary learning facilitates image restoration by simultaneously preserving significant representation and removing trivial perturbations. However, existing dictionary learning under strict ℓ0-norm based sparsity constraint lacks of convergence guarantees and suffers from the dilemma between block artifacts and degraded quality in restoring fine details, and could hamper the consequent deep unfolded networks (DUNs). To address these problems, in this paper, we propose the first ℓ0-regularized dictionary learning with a theoretical guarantee of global convergence that achieves globally consistent sparse approximation for image restoration. Specifically, we first formulate an ℓ0-norm based optimization for dictionary learning that simultaneously achieves sparse approximation of local patches and ensures global consistency between the recovered and observed images. Consequently, we develop ℓ0-regularized global-local dictionary learning (ℓ0-GLDL) that alternately achieves sparse code pursuit, local dictionary update, and global image reconstruction based on alternating proximal linearized method. We demonstrate in theory that ℓ0-GLDL converges globally to a critical point. Furthermore, we design a deep unfolded network by unrolling ℓ0 -GLDL into diverse subblocks to strictly realize alternating optimization for stable image restoration. Experimental results demonstrate that the proposed methods achieve state-of-the-art performance and outperform existing deep learning based methods in image restoration tasks such as image denoising, image deblurring, and image inpainting.

Image denoising remains a challenging problem due to the ill-posed nature of recovering clean images from noisy observations. Prior-based modeling plays a vital role in addressing this challenge. Low-rank priors effectively exploit non-local self-similarity by modeling correlations across similar images, but often over-smooth fine textures. In contrast, sparse priors, especially in the form of Convolutional Sparse Coding (CSC), excel at preserving high-frequency texture details, yet typically neglect the structure across images. Recent unfolded CSC networks have improved denoising performance by combining CSC with deep networks, but most of them rely solely on sparsity, overlooking the complementary low-rank structure information. To overcome these limitations, we propose UCSC-LR, the first interpretable unfolded CSC network that jointly leverages both sparse and low-rank priors within a unified architecture. UCSC-LR unrolls both the Iterative Shrinkage-Thresholding Algorithm (ISTA) and Singular Value Thresholding (SVT) to strictly implement alternating minimization, enabling simultaneous pursuit of sparse representations and low-rank reconstructions. A dedicated Fusion Net is introduced to adaptively integrate features from the two priors, allowing the model to preserve both texture and structural content. To further enhance performance on color image denoising, UCSC-LR incorporates a lightweight channel attention mechanism to capture inter-channel dependencies. With shared, pre-learned convolutional dictionaries and efficient parameterization, UCSC-LR achieves state-of-the-art performance with low model complexity. Extensive experiments on grayscale, blind, and color denoising tasks validate the effectiveness of the proposed method, consistently surpassing existing CSC-based and deep learning-based denoisers.

Existing diffusion models for inverse problems have demonstrated impressive performance but suffer from prohibitive sampling complexity due to lengthy iterative sampling procedures. While introducing pre-trained consistency models (CMs) as priors holds promise for fast and high-quality sampling, theoretical disparities between CMs and diffusion models remain, hindering the application of CMs in solving inverse problems. To address this issue, we propose a novel framework, named Dual Data Consistency Guided Consistency Model (DCCM), that for the first time to solve inverse problems with pretrained CM priors. We establish a denoising interpretation of CMs to set up the equivalence between CMs and denoisers and incorporate CM in a theoretically sound fashion. Consequently, we develop refined data consistency to facilitate optimization with CM priors and avoid local minima caused by the nonlinearity of degradation operators. Furthermore, we introduce the data consistency shortcut that leverages the manifold hypothesis to approximate refined data consistency and bypass backpropagation for enhanced sampling speed without reconstruction quality loss. Extensive experiments demonstrate DCCM achieves state-of-the-art performance in terms of reconstruction quality and sampling speed in a wide range tasks of image deblurring, super-resolution, and inpainting.

Light field (LF) data are widely used in the immersive representations of the 3D world. To record the light rays along with different directions, an LF requires much larger storage space and transmission bandwidth than a conventional 2D image with similar spatial dimension. In this paper, we propose a novel framework for light field image compression that leverages graph learning and dictionary learning to remove structural redundancies between different views. Specifically, to significantly reduce the bit-rates, only a few key views are sampled and encoded, whereas the remaining non-key views are reconstructed via the graph adjacency matrix learned from the angular patch. Furthermore, dictionary-guided sparse coding is developed to compress the graph adjacency matrices and reduce the coding overheads. To our best knowledge, this paper is the first to achieve compact representation of cross-view structural information via adaptive learning on graphs. Experimental results demonstrate that the proposed framework achieves better performance than the standardized HEVC-based codec.

The Cox proportional hazards model is a popular semi-parametric model for survival analysis. In this paper, we aim at developing a federated algorithm for the Cox proportional hazards model over vertically partitioned data (i.e., data from the same patient are stored at different institutions). We propose a novel algorithm, namely VERTICOX, to obtain the global model parameters in a distributed fashion based on the Alternating Direction Method of Multipliers (ADMM) framework. The proposed model computes intermediary statistics and exchanges them to calculate the global model without collecting individual patient-level data. We demonstrate that our algorithm achieves equivalent accuracy for the estimation of model parameters and statistics to that of its centralized realization. The proposed algorithm converges linearly under the ADMM framework. Its computational complexity and communication costs are polynomially and linearly associated with the number of subjects, respectively. Experimental results show that VERTICOX can achieve accurate model parameter estimation to support federated survival analysis over vertically distributed data by saving bandwidth and avoiding exchange of information about individual patients. The source code for VERTICOX is available at: https://github.com/daiwenrui/VERTICOX.

Conventional scalable compressive video sampling cannot sufficiently exploit the structured sparsity within video sequences. This paper proposes a novel quality scalable structured compressive video sampling (SS-CVS) framework with hierarchical subspace learning to support video transmission over heterogeneous network conditions. The proposed framework incorporates the union of data-driven subspaces (UoDS) model to introduce structured sparsity into sensing matrix for progressive acquisition of measurements. Hierarchical subspace learning is developed to generate the subspaces with their bases based on adaptive subspace clustering in a progressive fashion. Consequently, two hierarchical structures are derived to enable progressive mapping of subspaces and bases on the structured sensing matrices to support quality scalability. To guarantee the convergence of hierarchical subspace learning, the training set is updated with the adaptive group set from the reconstructed reference frames. It is demonstrated that SS-CVS can guarantee stable recovery for each quality layer under the constraints of block restricted isometric property (RIP). Furthermore, the proposed SS-CVS model is generalized to tensor subspaces for scalable compressive sampling of high-dimensional signals. Experimental results demonstrate that the proposed algorithm can achieve quality scalabilities with an improved reconstructed performance in comparison to the state-of-the-art scalable compressive video sampling methods.

Due to the popularity of 3D videos, 2D-to-3D video conversion has become a hot research topic for the past few years. The most critical issue in 3D video synthesis is the estimation of depth maps for the video frames. Numerous efforts have been devoted in fully automatic and semi-automatic depth estimation approaches, although the discontinuity of depth field and the ambiguity of motion boundary are still the main challenges in depth estimation. This paper proposes a semi-automatic structure-aware sparse-to-dense depth estimation method, which leverages the tensor voting at two different levels to propagate depth across frames. In the first level, a 4D tensor voting is performed to remove outliers caused by inaccurate motion estimation. Noticing that the 4D tensors of correctly matched points should lie on the smooth layer in the manifold, we utilize the variety saliency defined by the eigen-system of the tensor for outlier removal. In the second level, a high-dimensional tensor voting algorithm, incorporating spatial location, motion, and color into the tensor representation, is devised to propagate the depth from the sparse points to the entire image domain. By projecting the input feature into the tangent space, the relation between the location, motion, color, and the depth can be established by voting process. Extensive experiments on public data set validate the effectiveness of the proposed method in comparison with state-of-the-art depth estimation approaches.

The nonlinear recovery is not promising in accuracy and speed, which limits the practical usage of compressed sensing (CS). This paper proposes a deep learning-based CS framework which leverages a deep convolutional auto-encoder for image sensing and recovery. The utilized auto-encoder architecture consists of three components: the fully convolutional network acts as an adaptive measurement matrix generator in the encoder; while in the decoder, the deconvolution network and refined reconstruction network are learned for intermediate and final recovery, respectively. Different from most previous work focusing on the block-wise manner to reduce implementation cost but result in blocky artifacts, our adaptive measurement matrix is applicable to any size of scene image and the decoder network reconstructs the whole image efficiently without any blocky artifacts. Moreover, dense connectivity is leveraged to combine multi-level features and alleviate the vanishing-gradient problem in the refined reconstruction network which boosts the performance on image recovery. Compared to the state-of-the-art methods, our algorithm improves more than 0.8 dB in average PSNR.

Demanding for efficient compression and storage of DNA sequences has been rising with the rapid growth of DNA sequencing technologies. Existing reference-based algorithms map all patterns to regions found in the reference sequence, which lead to redundancy of incomplete similarity. This paper proposes an efficient reference-based method for DNA sequence compression that integrates FM-index and complementary context models to improve compression performance. The proposed method introduces FM-index to represent the full-text matching for exact repeats between the target and reference sequences. For unmatched symbols, complementary context models are leveraged to make weighted estimation conditioned on variable-order contexts. Reversed reference index is used to guarantee the longest match of variable-length substrings. Experimental results show that the proposed method can achieve a 213-fold compression ratio when tested on the first Korean personal genome sequence data set.

Tensor-based compressive sensing (CS) can preserve the intrinsic multidimensional structures with a reduced computational complexity. However, its recovery performance is degraded by simple sparsity. This paper proposes an efficient recovery algorithm GT-ADMM to solve a nonconvex optimization problem for tensor-based CS with group sparsity. Group-sparse representations of tensors is derived based on the Kronecker product of adaptively trained basis. The proposed algorithm incorporates alternating direction method of multipliers (ADMM) to obtain desirable recovery quality with improved efficiency. It requires few degrees of freedom to achieve tensor recovery with a guarantee of minimized approximation error. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art tensor-based methods in compressive video sampling.

Conventional Compressive Sensing (CS) obscures the intrinsic structures of multidimensional signals with the vectorized representation. Although tensor-based CS methods can preserve the intrinsic multidimensional structures with reduced computational complexity, their sampling efficiency and recovery performance are degraded with the assumption of standard/simple sparsity. This paper proposes a general and adaptive model that incorporates structured sparsity into tensor representation to fit the varying nonstationary statistics of multidimensional signals. To guarantee the block sparsity, subspace clustering is adopted to adaptively generate the union of tensor subspaces with its basis of each tensor subspace learned for optimized representation. For sampled tensors, the stable recovery algorithm is developed to achieve desirable recovery performance using fewer degrees of freedom. Moreover, the proposed model inherits the merit from tensor-based CS to alleviate the computational and storage burden in sampling and recovery. Experimental results demonstrate that the proposed model can achieve better recovery performance in video sampling in comparison to the state-of-the-art tensor-based method.

Recently, 2D-to-3D video conversion has raised great interest because of the increasing demand of 3D video contents. A critical component in semi-automatic methods is to estimate the depth information of non-key frames from key frames. To overcome the sensitiveness to occlusion in existing schemes, a depth propagation method is proposed in this paper where tensor voting is leveraged to eliminate occlusion points, thereby derive accurate sparse depth. Furthermore, high dimensional tensor is constructed with coordinate, motion and color features to represent points in the sparse depth. A dense depth can be generated via tensor-voting based interpolation. It is robust against object occlusion and inaccurate motion estimation because tensor voting can efficiently make denoising and capture the structures. Experiment results demonstrate that the proposed method outperforms state-of-the-art semi-automatic techniques.

OBJECTIVE: To develop an accurate logistic regression (LR) algorithm to support federated data analysis of vertically partitioned distributed data sets. MATERIAL AND METHODS: We propose a novel technique that solves the binary LR problem by dual optimization to obtain a global solution for vertically partitioned data. We evaluated this new method, VERTIcal Grid lOgistic regression (VERTIGO), in artificial and real-world medical classification problems in terms of the area under the receiver operating characteristic curve, calibration, and computational complexity. We assumed that the institutions could "align" patient records (through patient identifiers or hashed "privacy-protecting" identifiers), and also that they both had access to the values for the dependent variable in the LR model (eg, that if the model predicts death, both institutions would have the same information about death). RESULTS: The solution derived by VERTIGO has the same estimated parameters as the solution derived by applying classical LR. The same is true for discrimination and calibration over both simulated and real data sets. In addition, the computational cost of VERTIGO is not prohibitive in practice. DISCUSSION: There is a technical challenge in scaling up federated LR for vertically partitioned data. When the number of patients m is large, our algorithm has to invert a large Hessian matrix. This is an expensive operation of time complexity O(m(3)) that may require large amounts of memory for storage and exchange of information. The algorithm may also not work well when the number of observations in each class is highly imbalanced. CONCLUSION: The proposed VERTIGO algorithm can generate accurate global models to support federated data analysis of vertically partitioned data.

Existing sparse representation with subspace learning is hampered by the intersection of subspaces of bases. With structured sparsity to enable the prior knowledge of signal statistics, this paper proposes a novel compressive video sampling by subspace learning to minimize the intersection of subspaces. As the measurement, the block coherence is optimized with the regularized learning to generate a class of independent bases associated with the subspaces. Thus, the proposed framework can make a compact block sparse representation based on the derived basis in an efficient and adaptive manner. The block-based recovery of video sequences is demonstrated to be stable under the constraint of block restricted isometric property (RIP). Experimental results show that the proposed method outperforms existing compressive video sampling schemes.

The standard Compressive Sensing (CS) theory indicates that robust signals recovery can be obtained from just a few collection of incoherent projections. To further decrease the necessary measurements, an alternative to the generic CS framework assumes that signals lie on a union of subspaces (UoS). However, UoS model is limited to the specific type of signal regularity. This paper considers a more general and adaptive model which presumes that signals lie on a union of data-driven subspaces (UoDS). The UoDS model inherits the merit from UoS that signals have structural sparse representation. Meanwhile, it allows to recover signals using fewer degrees of freedom for a desirable recovery quality than UoS. To construct the UoDS model, a subspace clustering method is utilized to form an adaptive group set. The corresponding adaptive basis is learned by applying a linear subspace learning (LSL) method to each group. A corresponding recovery algorithm with provable performance is also given. Experiment results demonstrate that the proposed model for video sampling is valid and applicable.

Recently, compressive sampling (CS) is an active research field of signal processing. To further decrease the necessary measurements and get more efficient recovery of a signal x, recent approaches assume that x lives in a union of subspaces (UoS). Unlike previous approaches, this paper proposes a novel method to sample and recover an unknown signal from a union of data-driven subspaces (UoDS). Instead of a fix set of supports, this UoDS is learned from classified signal series which are uniquely formed by block matching. The basis of these data-driven subspaces is regularized after dimensionality reduction by principal component extraction. A corresponding recovery solution with provable performance guarantees is also given, which takes full advantage of block-sparsity structure and improves the recovery efficiency. In practice, the proposed scheme is fulfilled to sample and recover frames in video sequences. The experimental results demonstrate that the proposed video sampling behaves better performance in sampling and recovery than the classical CS.