Michael Elad

$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signal...

Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ ¹ minimization

Given a dictionary D = { d k } of vectors d k , we seek to represent a signal S as a linear combination S = ∑ k γ( k ) d k , with scalar coefficients γ ( k ). In particular, we ...

Stable recovery of sparse overcomplete representations in the presence of noise

Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in ...

Image decomposition via the combination of sparse representations and a variational approach

The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years, several pioneeri...

Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)

A generalized uncertainty principle and sparse representation in pairs of bases

An elementary proof of a basic uncertainty principle concerning pairs of representations of R/sup N/ vectors in different orthonormal bases is provided. The result, slightly str...

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse ...