We propose a new approach to robustly retrieve the exit wave of an extended sample from its coherent diffraction pattern by exploiting sparsity of the sample's edges. This approach enables imaging of an extended sample with a single view, without ptychography. We introduce nonlinear optimization methods that promote sparsity, and we derive update rules to robustly recover the sample's exit wave...

Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from a fusion frame. We use a block sparsity model for fusion frames and then show that sparse signals under this model can be compressively sampled and reconstr...

We consider the recovery of jointly sparse multichannel signals from incomplete measurements using convex relaxation methods. Worst case analysis is not able to provide insights into why joint sparse recovery is superior to applying standard sparse reconstruction methods to each channel individually. Therefore, we analyze an average case by imposing a probability model on the measured signals. ...

We study the compressed sensing (CS) signal estimation problem where an input is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the observed signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a s...

EDICS Category: SAS-MALN Abstract—The performance of sparse signal recovery can be improved if both sparsity and correlation structure of signals can be exploited. One typical correlation structure is intra-block correlation in block sparse signals. To exploit this structure, a framework, called block sparse Bayesian learning (BSBL) framework, has been proposed recently. Algorithms derived from...

Memory-based collaborative filtering is the most popular approach to build recommender systems. Despite its success in many applications, it still suffers from several major limitations, including data sparsity. Sparse data affect the quality of the user similarity measurement and consequently the quality of the recommender system. In this paper, we propose a novel user similarity measure based...

We develop a novel sparse low-rank block (SLoB) signal recovery framework that simultaneously exploits sparsity and low-rankness to accurately identify peptides (fragments of proteins) from biological samples via tandem mass spectrometry (TMS). To efficiently perform SLoB-based peptide identification, we propose two novel recovery algorithms, an exact iterative method and an approximate greedy ...

The problem of recovering the sparse and low-rank components of a matrix captures a broad spectrum of applications. Authors in [4] proposed the concept of ”rank-sparsity incoherence” to characterize the fundamental identifiability of the recovery, and derived practical sufficient conditions to ensure the high possibility of recovery. This exact recovery is achieved via solving a convex relaxati...

Accelerated MRI techniques reduce signal acquisition time by undersampling k-space. A fundamental problem in accelerated MRI is the recovery of quality images from undersampled k-space data. Current state-of-the-art recovery algorithms exploit the spatial and temporal structures in underlying images to improve the reconstruction quality. In recent years, compressed sensing theory has helped for...

For Gaussian sampling matrices, we provide bounds on the minimal number of measurements m required to achieve robust weighted sparse recovery guarantees in terms of how well a given prior model for the sparsity support aligns with the true underlying support. Our main contribution is that for a sparse vector x ∈ R supported on an unknown set S ⊂ {1, 2, . . . , N} with |S| ≤ k, if S has weighted...