Related papers: Robust width: A characterization of uniformly stab…

We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…

Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the…

In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…

We study the problem of distributed and rate-adaptive feature compression for linear regression. A set of distributed sensors collect disjoint features of regressor data. A fusion center is assumed to contain a pretrained linear regression…

This paper is concerned with the hard thresholding operator which sets all but the $k$ largest absolute elements of a vector to zero. We establish a {\em tight} bound to quantitatively characterize the deviation of the thresholded solution…

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage…

With the advent of multi-coil imaging and compressed sensing, a number of model based reconstruction algorithms have been created. They incorporate a multitude of different regularization functions based on physics, observed phenomenology,…

It is well established in the compressive sensing (CS) literature that sensing matrices whose elements are drawn from independent random distributions exhibit enhanced reconstruction capabilities. In many CS applications, such as…

Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…

Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…

This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…

Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…

The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…

We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing…

We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…

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…