L1 minimization applied to two sparse signals that can be described as sums of elementary functions

摘要

Compressive sampling is a technique used in digital signal processing, which allows for the capture of high resolution physical signals from relatively few measurements. This technique is illustrated here for two simple cases: a signal to be that can be expressed as a sum of three sine functions and another one that can be expressed as a sum of three Bessel functions of the first kind. In order to perform a compressive sampling one must use correct measurement vectors and this is a quite complicated problem. In this paper a simple algorithm for obtaining the correct measurement vectors for illustration and pedagogical purposes is shown.