Related papers: Recovery of Missing Samples Using Sparse Approxima…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Restoration of images degraded by spatially varying blurs is an issue of increasing importance in the context of photography, satellite or microscopy imaging. One of the main difficulty to solve this problem comes from the huge dimensions…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from…
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.…
In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the $q$-ratio sparsity. When $1 < q \leq \infty$, both the theoretical analysis based on $q$-ratio constrained minimal singular…
In this paper, we propose a method for image block loss restoration based on the notion of sparse representation. We use the sparsity pattern as side information to efficiently restore block losses by iteratively imposing the constraints of…
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…
In the area of near-field millimeter-wave imaging, the generalized sparse array synthesis (SAS) method is in great demand. The traditional methods usually employ the greedy algorithms, which may have the convergence problem. This paper…
One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. In many…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…
In this work we address the problem of blindly reconstructing compressively sensed signals by exploiting the co-sparse analysis model. In the analysis model it is assumed that a signal multiplied by an analysis operator results in a sparse…
This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…