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The compressed sensing (CS) framework leverages the sparsity of MR images to reconstruct from undersampled acquisitions. CS reconstructions involve one or more regularization parameters that weigh sparsity in transform domains against…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
Designing computational experiments involving $\ell_1$ minimization with linear constraints in a finite-dimensional, real-valued space for receiving a sparse solution with a precise number $k$ of nonzero entries is, in general, difficult.…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear…
Magnetic particle imaging (MPI) data is commonly reconstructed using a system matrix acquired in a time-consuming calibration measurement. The calibration approach has the important advantage over model-based reconstruction that it takes…
We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m x n matrices A such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD…
We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the…
The paper introduces a framework for the recoverability analysis in compressive sensing for imaging applications such as CI cameras, rapid MRI and coded apertures. This is done using the fact that the Spherical Section Property (SSP) of a…
This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm that leverages a trained generative model to enhance the signal reconstruction performance. The generator, a…
Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available…
In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single--terminal setup as well as in a multi--terminal setup consisting of…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…