Related papers: Interpolation via weighted $l_1$ minimization
$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…
Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be…
Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and…
We develop a Recursive $\mathcal{L}_1$-Regularized Least Squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
First-principles based lattice models allow the modeling of ab initio thermodynamics of crystalline mixtures for applications such as the construction of phase diagrams and the identification of ground state atomic orderings. The recent…
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…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…
Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical…
Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…
We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…
This paper is motivated by structured sparsity for deep neural network training. We study a weighted group L0-norm constraint, and present the projection and normal cone of this set. Using randomized smoothing, we develop zeroth and…
Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\ell_1$-regularized…
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…