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Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is…

Compressed sensing (CS) in Magnetic resonance Imaging (MRI) essentially involves the optimization of 1) the sampling pattern in k-space under MR hardware constraints and 2) image reconstruction from the undersampled k-space data. Recently,…

In this paper we study the performance of image reconstruction methods from incomplete samples of the 2D discrete Fourier transform. Inspired by requirements in parallel MRI, we focus on a special sampling pattern with a small number of…

In recent years, compressed sensing (CS) has been applied in the field of synthetic aperture radar (SAR) imaging and shows great potential. The existing models are, however, based on application of the sensing matrix acquired by the exact…

Network reconstruction is important to the understanding and control of collective dynamics in complex systems. Most real networks exhibit sparsely connected properties, and the connection parameter is a signal (0 or 1). Well-known…

The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Compressive sensing (CS) has been studied and applied in structural health monitoring for wireless data acquisition and transmission, structural modal identification, and spare damage identification. The key issue in CS is finding the…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this paper, we consider the problem of optimizing the sub-sampling pattern in a data-driven fashion. Since…

Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower…

We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown that $\textit{O}(kdn\| \boldsymbol{\alpha}\|_{\infty}^{2})$…

Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects…

In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…

Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively…

This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and…

Scene-aware Adaptive Compressive Sensing (ACS) has attracted significant interest due to its promising capability for efficient and high-fidelity acquisition of scene images. ACS typically prescribes adaptive sampling allocation (ASA) based…

Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…

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…