Astronomical Data Analysis and Sparsity: From Wavelets to Compressed Sensing

Sparsity-optimized Harmonic Wavelets for Compressed Sensing MRI

Compressed sensing and sparsity in photoacoustic tomography

Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this issue using techniques of compressed sensing. We demonstrate, that the number of measurements can significantly be reduced by allowing general linear measur...

Compressed sensing, sparsity, and dimensionality in neuronal information processing and data analysis.

The curse of dimensionality poses severe challenges to both technical and conceptual progress in neuroscience. In particular, it plagues our ability to acquire, process, and model high-dimensional data sets. Moreover, neural systems must cope with the challenge of processing data in high dimensions to learn and operate successfully within a complex world. We review recent mathematical advances ...

Sparsity Pattern Recovery in Compressed Sensing

Sparsity Pattern Recovery in Compressed Sensing by Galen Reeves Doctor of Philosophy in Engineering — Electrical Engineering and Computer Sciences University of California, Berkeley Professor Michael Gastpar, Chair The problem of recovering sparse signals from a limited number of measurements is now ubiquitous in signal processing, statistics, and machine learning. A natural question of fundame...

Compressed Sensing: “When sparsity meets sampling”∗

The recent theory of Compressed Sensing (Candès, Tao & Romberg, 2006, and Donoho, 2006) states that a signal, e.g. a sound record or an astronomical image, can be sampled at a rate much smaller than what is commonly prescribed by Shannon-Nyquist. The sampling of a signal can indeed be performed as a function of its “intrinsic dimension” rather than according to its cutoff frequency. This chapte...