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Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…
This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain…
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…
Conventional compressive sensing (CS) reconstruction is very slow for its characteristic of solving an optimization problem. Convolu- tional neural network can realize fast processing while achieving compa- rable results. While CS image…
This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
Compressed sensing with sparse frame representations is seen to have much greater range of practical applications than that with orthonormal bases. In such settings, one approach to recover the signal is known as $\ell_1$-analysis. We…
The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…
Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…
This paper surveys recent work in applying ideas from graphical models and message passing algorithms to solve large scale regularized regression problems. In particular, the focus is on compressed sensing reconstruction via ell_1 penalized…
Many service computing applications require real-time dataset collection from multiple devices, necessitating efficient sampling techniques to reduce bandwidth and storage pressure. Compressive sensing (CS) has found wide-ranging…
Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…
In x-ray computed tomography (CT) it is generally acknowledged that reconstruction methods exploiting image sparsity allow reconstruction from a significantly reduced number of projections. The use of such reconstruction methods is…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
We develop a new compressive sensing (CS) inversion algorithm by utilizing the Gaussian mixture model (GMM). While the compressive sensing is performed globally on the entire image as implemented in our lensless camera, a low-rank GMM is…
Recent developments of new medical treatment techniques put challenging demands on ultrasound imaging systems in terms of both image quality and raw data size. Traditional sampling methods result in very large amounts of data, thus,…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…