Gravimetric Detection by Compressed Sensing

We address the problem of identifying underground anomalies (e.g holes) based on gravity measurements. Our approach makes general assumptions about the shape of the hole, e.g that it can described by few wavelet coefficients. Such assumptions are known under the name of sparsity assumptions. Based on the recently developed compressed sensing (CS) methodology we output an estimate mass density over the whole domain of interest in one global optimization step. Our algorithms performance is promising on medium scale problems, even though the theoretical assumptions underlying CS do not hold for gravity problems of this kind.