Sparse signal and image recovery from Compressive Samples

In this paper we present an introduction to Compressive Sampling (CS), an emerging model-based framework for data acquisition and signal recovery based on the premise that a signal having a sparse representation in one basis can be reconstructed from a small number of measurements collected in a second basis that is incoherent with the first. Interestingly, a random noise-like basis will suffice for the measurement process. We will overview the basic CS theory, discuss efficient methods for signal reconstruction, and highlight applications in medical imaging

Imaging via Compressive Sampling [Introduction to compressive sampling and recovery via convex programming]

There is an extensive body of literature on image compression, but the central concept is straightforward: we transform the image into an appropriate basis and then code only the important expansion coefficients. The crux is finding a good transform, a problem that has been studied extensively from both a theoretical [14] and practical [25] standpoint. The most notable product of this research is the wavelet transform [9], [16]; switching from sinusoid-based representations to wavelets marked a watershed in image compression and is the essential difference between the classical JPEG [18] and modern JPEG-2000 [22] standards. Image compression algorithms convert high-resolution images into a relatively small bit streams (while keeping the essential features intact), in effect turning a large digital data set into a substantially smaller one. But is there a way to avoid the large digital data set to begin with? Is there a way we can build the data compression directly into the acquisition? The answer is yes, and is what compressive sampling (CS) is all about