相关论文: Fast Linearized Bregman Iteration for Compressive …
Compressed sensing is a central topic in signal processing with myriad applications, where the goal is to recover a signal from as few observations as possible. Iterative re-weighting is one of the fundamental tools to achieve this goal.…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
This paper presents three distributed techniques to find a sparse solution of the underdetermined linear problem $\textbf{g}=\textbf{Hu}$ with a norm-1 regularization, based on the Alternating Direction Method of Multipliers (ADMM). These…
We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \, \rho =b$, where $A$ is an $N\times K$ measurement matrix. We assume…
We propose a deconvolution algorithm for images blurred and degraded by a Poisson noise. The algorithm uses a fast proximal backward-forward splitting iteration. This iteration minimizes an energy which combines a \textit{non-linear} data…
Magnetic Resonance Imaging (MRI) is one of the fields that the compressed sensing theory is well utilized to reduce the scan time significantly leading to faster imaging or higher resolution images. It has been shown that a small fraction…
We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
Methods exploiting sparsity have been popular in imaging and signal processing applications including compression, denoising, and imaging inverse problems. Data-driven approaches such as dictionary learning and transform learning enable one…
This article addresses the image denoising problem in the situations of strong noise. We propose a dual sparse decomposition method. This method makes a sub-dictionary decomposition on the over-complete dictionary in the sparse…
Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…
In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…
Noisy images processing is a fundamental task of computer vision. The first example is the detection of faint edges in noisy images, a challenging problem studied in the last decades. A recent study introduced a fast method to detect faint…
Ultra-fine-grained image recognition (UFGIR) categorizes objects with extremely small differences between classes, such as distinguishing between cultivars within the same species, as opposed to species-level classification in fine-grained…
Prior-based methods for low-light image enhancement often face challenges in extracting available prior information from dim images. To overcome this limitation, we introduce a simple yet effective Retinex model with the proposed edge…
A novel probabilistic sparsity-promoting method for robust near-field (NF) antenna characterization is proposed. It leverages on the measurements-by-design (MebD) paradigm and it exploits some a-priori information on the antenna under test…
In this paper, we propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. This accelerated algorithm is based on the fact that the linearized Bregman (LB)…