Related papers: Compressed Sensing with General Frames via Optimal…
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…
The practice of compressed sensing suffers importantly in terms of the efficiency/accuracy trade-off when acquiring noisy signals prior to measurement. It is rather common to find results treating the noise affecting the measurements,…
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…
Analysis $\ell_1$-recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the…
We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
The use of generalized LASSO is a common technique for recovery of structured high-dimensional signals. Each generalized LASSO program has a governing parameter whose optimal value depends on properties of the data. At this optimal value,…
Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition…
In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
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…
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…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
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…