We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main… (More)

The typical paradigm for obtaining a compressed version of a discrete signal represented by a vector x ∈ R is to choose an appropriate basis, compute the coefficients of x in this basis, and then… (More)

Under certain conditions (known as the restricted isometry property, or RIP) on the m N matrix ˆ (where m < N ), vectors x 2 RN that are sparse (i.e., have most of their entries equal to 0) can be… (More)

PURPOSE
To confirm the promising phase II results of docetaxel monotherapy, this phase III trial was conducted of chemotherapy for patients with advanced non-small-cell lung cancer (NSCLC) who had… (More)

Parametric partial differential equations are commonly used to model physical systems. They also arise when Wiener chaos expansions are used as an alternative to Monte Carlo when solving stochastic… (More)

In recent years, various nonlinear methods have been proposed and deeply investigated in the context of nonparametric estimation: shrinkage methods [21], locally adaptive bandwidth selection [16] and… (More)

Given a Banach space X and one of its compact sets F , we consider the problem of finding a good n dimensional space Xn ⊂ X which can be used to approximate the elements of F . The best possible… (More)

Tree approximation is a new form of nonlinear approximation which appears naturally in some applications such as image processing and adaptive numerical methods. It is somewhat more restrictive than… (More)

We show how two fundamental results in analysis related to n-widths and Compressed Sensing are intimately related to the Johnson-Lindenstrauss lemma. Our elementary approach is based on the same… (More)

We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is “almost” characterized by… (More)