Related papers: Compressive Spectral Renormalization Method
Patch-based sparse representation modeling has shown great potential in image compressive sensing (CS) reconstruction. However, this model usually suffers from some limits, such as dictionary learning with great computational complexity,…
We present a computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS). CS theory requires solving a convex constrained minimization problem. We…
The spectral renormalization method was introduced by Ablowitz and Musslimani in 2005, [Opt. Lett. 30, pp. 2140-2142] as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems.…
While the recent theory of compressed sensing provides an opportunity to overcome the Nyquist limit in recovering sparse signals, a solution approach usually takes a form of inverse problem of the unknown signal, which is crucially…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…
Compressed Sensing MRI reconstructs images of the body's internal anatomy from undersampled measurements, thereby reducing scan time. Recently, deep learning has shown great potential for reconstructing high-fidelity images from highly…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…
Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee…
Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…
We develop a method for sparse image reconstruction from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident-energy spectrum are unknown. We obtain a…
An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the…
A signal is sparse in one of its representation domain if the number of nonzero coefficients in that domain is much smaller than the total number of coefficients. Sparse signals can be reconstructed from a very reduced set of…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a., compressive phase retrieval), emerges naturally in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex…
Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
The mathematical theory of super-resolution developed recently by Cand\`{e}s and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set…
Pre-trained large models attract widespread attention in recent years, but they face challenges in applications that require high interpretability or have limited resources, such as physical sensing, medical imaging, and bioinformatics.…