Designing Incoherent Dictionaries for Compressed Sensing: Algorithm Comparison

INTERDISCIPLINARY MATHEMATICS INSTITUTE 2010 : 01 Orthogonal super greedy algorithm and application in compressed sensing IMI

The general theory of greedy approximation is well developed. Much less is known about how specific features of a dictionary can be used for our advantage. In this paper we discuss incoherent dictionaries. We build a new greedy algorithm which is called the Orthogonal Super Greedy Algorithm (OSGA). OSGA is more efficient than a standard Orthogonal Greedy Algorithm (OGA). We show that the rates ...

Frames for compressed sensing using coherence

We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satised. Moreover, we give better estimations then the ones given recently by Cai, Wang and Xu.

Accelerating Magnetic Resonance Imaging through Compressed Sensing Theory in the Direction space-k

Magnetic Resonance Imaging (MRI) is a noninvasive imaging method widely used in medical diagnosis. Data in MRI are obtained line-by-line within the K-space, where there are usually a great number of such lines. For this reason, magnetic resonance imaging is slow. MRI can be accelerated through several methods such as parallel imaging and compressed sensing, where a fraction of the K-space lines...

Adaptive Compressed Image Sensing Using Dictionaries

In recent years, the theory of Compressed Sensing has emerged as an alternative for the Shannon sampling theorem, suggesting that compressible signals can be reconstructed from far fewer samples than required by the Shannon sampling theorem. In fact the theory advocates that non-adaptive, ‘random’ functionals are in some sense optimal for this task. However, in practice, Compressed Sensing is v...

Designing Optimal Projections for Compressed Sensing: Algorithm Comparison