Related papers: A Tight Bound of Hard Thresholding
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…
The recent work of \cite{CRT,DonohoPol} rigorously proved (in a large dimensional and statistical context) that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. While the coherence is easy to compute, it can lead to rather…
An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques (NST+HT+FB). The main contribution of this…
In this paper, we propose a general framework for the asymptotic analysis of node-based verification-based algorithms. In our analysis we tend the signal length $n$ to infinity. We also let the number of non-zero elements of the signal $k$…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
We provide a new information-theoretic generalization error bound that is exactly tight (i.e., matching even the constant) for the canonical quadratic Gaussian (location) problem. Most existing bounds are order-wise loose in this setting,…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
Positive definite (p.d.) matrices arise naturally in many areas within mathematics and also feature extensively in scientific applications. In modern high-dimensional applications, a common approach to finding sparse positive definite…
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations.…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…
Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a…
In our recent work \cite{StojnicCSetam09} we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved that if the number of equations in the system is…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…