Related papers: High-dimensional sparse recovery from function sam…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage…
In this paper, we account for approaches of sparse recovery from large underdetermined linear models with perturbation present in both the measurements and the dictionary matrix. Existing methods have high computation and low efficiency.…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
It has been found that radar returns of extended targets are not only sparse but also exhibit a tendency to cluster into randomly located, variable sized groups. However, the standard techniques of Compressive Sensing as applied in radar…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal…
This study addresses the blind deconvolution problem with modulated inputs, focusing on a measurement model where an unknown blurring kernel $\boldsymbol{h}$ is convolved with multiple random modulations…
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
We investigate the sparse functional identification of complex cells and the decoding of visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm of both temporal and spatio-temporal stimuli is formulated as a…
In this paper, we study the number of measurements required to recover a sparse signal in ${\mathbb C}^M$ with $L$ non-zero coefficients from compressed samples in the presence of noise. For a number of different recovery criteria, we prove…
$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…
In this paper, we consider recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding,…
The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
Non-local self-similarity and sparsity principles have proven to be powerful priors for natural image modeling. We propose a novel differentiable relaxation of joint sparsity that exploits both principles and leads to a general framework…
In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has…