Many common image-processing tasks (such as denoising, deblurring etc...) involve total variation (TV) based optimization problems. One
of the newest and most exciting application of TV-based imaging is the field of compressed sensing (CS), which allows high-resolution images
to be constructed from small amounts of data. In this talk, we will give a brief introduction to CS and other TV regularized problems related to MRI. We will then discuss a simple and highly efficient
numerical scheme for computing solutions to these problems. Finally, we will present some CS imaging results, and discuss how CS techniques
can lead to faster scan times, and higher image quality.