Related papers: Interpolation via weighted $l_1$ minimization

The $\ell_1$ norm is the tight convex relaxation for the $\ell_0$ "norm" and has been successfully applied for recovering sparse signals. For problems with fewer samplings, one needs to enhance the sparsity by nonconvex penalties such as…

We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…

Pruning the weights of neural networks is an effective and widely-used technique for reducing model size and inference complexity. We develop and test a novel method based on compressed sensing which combines the pruning and training into a…

We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…

The main contribution of the paper is a new approach to subspace clustering that is significantly more computationally efficient and scalable than existing state-of-the-art methods. The central idea is to modify the regression technique in…

In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting…

Using tools from semiclassical analysis, we give weighted L^\infty estimates for eigenfunctions of strictly convex surfaces of revolution. These estimates give rise to new sampling techniques and provide improved bounds on the number of…

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…

Sparsity, defined as the presence of missing or zero values in a dataset, often poses a major challenge while operating on real-life datasets. Sparsity in features or target data of the training dataset can be handled using various…

From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…

Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…

Compressed Neural Networks have the potential to enable deep learning across new applications and smaller computational environments. However, understanding the range of learning tasks in which such models can succeed is not well studied.…

We consider the sparse polynomial approximation of a multivariate function on a tensor product domain from samples of both the function and its gradient. When only function samples are prescribed, weighted $\ell^1$ minimization has recently…

In compressed sensing problems, $\ell_1$ minimization or Basis Pursuit was known to have the best provable phase transition performance of recoverable sparsity among polynomial-time algorithms. It is of great theoretical and practical…

To recover a sparse signal from an underdetermined system, we often solve a constrained L1-norm minimization problem. In many cases, the signal sparsity and the recovery performance can be further improved by replacing the L1 norm with a…