ABSTRACT

Large amounts of data are often redundant and methods for compressing these data sets play an increasingly important role in a number of applications. The basic idea is to find ways to expand the data vector as a superposition of known vectors, so that only a few of the coefficients are nonzero. Much of the research in this field goes under the names compressed sensing and compressed sampling (CS) [67]. The key notion in CS is sparseness. The JPEG technology uses such an approach to represent images as a superposition of sinusoids and wavelets. For applications such as medical imaging, CS provides a means of reducing radiation dosage to the patient without sacrificing image quality. An important aspect of CS is finding sparse solutions of underdetermined systems of linear equations, which can often be accomplished by one-norm minimization. The best reference on CS to date is probably [16].