Data-driven diagnosis for compressed sensing algorithms

Abstract

A data-driven diagnosis approach is developed for compressed sensing algorithms to objectively detect the failure of each algorithm and the insufficiency of data. Compressed sensing enables us to reduce the amount of data to a threshold; however, the problem is that no one can tell where the threshold is in practice. The approach is based on the statistical technique of cross-validation, in which part of the data is set aside as a validation dataset to assess the results of the analysis of the remaining data with an objective algorithm. The relation between cross-validation error and the size ratio of the whole dataset and validation dataset is evaluated and compared with a power-law relation to determine whether data analysis was successfully conducted. After summarizing our recent theoretical work on the first application of the approach to the basis pursuit method, it is shown by numerical experiments that the approach is universally applicable to several other algorithms.