#### Publication Date

3-2013

#### Abstract

In practice, we usually have partial information; as a result, we have several different possibilities consistent with the given measurements and the given knowledge. For example, in geosciences, several possible density distributions are consistent with the measurement results. It is reasonable to select the simplest among such distributions. A general solution can be described, e.g., as a linear combination of basic functions. A natural way to define the simplest solution is to select a one for which the number of the non-zero coefficients c_{i} is the smallest. The corresponding "l_{0}-optimization" problem is non-convex and therefore, difficult to solve. As a good approximation to this problem, Candes and Tao proposed to use a solution to the convex l_{1} optimization problem |c_{1}| + ... + |c_{n}| --> min. In this paper, we provide a geometric explanation of why l_{1} is indeed the best convex approximation to l_{0}.

## Comments

Technical Report: UTEP-CS-13-18

To appear in

Journal of Uncertain Systems, 2013, Vol. 7.