In recent years, inspired by the success of compressive sensing, interest has been drawn to TV-minimization as a mean to reconstruct sparse measures. Possible applications include spike resolution in imaging. The (measure-)TV minimization problem has nice theoretical features, but since it is infinite dimensional, the numerical resolution of it is not trivial.
In this talk, we will discuss a class of algorithms called exchange algorithms for solving the TV-minimization problem. We will see that one version of it is equivalent to the celebrated conditional gradient method. We will also discuss a condition, tailormade for the sparse recovery problem, under which a particular version of the method converges at linear speed.