Related papers: Support Recovery of Sparse Signals
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
We study sparse recovery when observations come from mixed-quality sources: a small collection of high-quality measurements with small noise variance and a larger collection of lower-quality measurements with higher variance. For this…
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…
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…
This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower…
The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…
Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard…
Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…
This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
One-bit compressed sensing (1bCS) addresses the recovery of sparse signals from highly quantized measurements, retaining only the sign of each linear measurement. In the support recovery setting, the goal is to identify $\text{supp}(x)$,…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
Orthogonal matching pursuit (OMP) is a greedy algorithm popularly being used for the recovery of sparse signals. In this paper, we study the performance of OMP for support recovery of sparse signal under noise. Our analysis shows that under…