Courant Institute of Mathematical Sciences

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of fun...

Singularity detection and processing with wavelets

The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across ...

Learning Hierarchical Features for Scene Labeling

Scene labeling consists of labeling each pixel in an image with the category of the object it belongs to. We propose a method that uses a multiscale convolutional network traine...

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws

Image denoising using scale mixtures of gaussians in the wavelet domain

We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coef...

Multiresolution approximations and wavelet orthonormal bases of 𝐿²(𝑅)

A multiresolution approximation is a sequence of embedded vector spaces <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altt...

Adaptive greedy approximations

Strange kinetics

On the Foundations of Relaxation Labeling Processes

A large class of problems can be formulated in terms of the assignment of labels to objects. Frequently, processes are needed which reduce ambiguity and noise, and select the be...

Convolutional Learning of Spatio-temporal Features