Empirical risk minimization-based analysis of segmented compressed sampling

A new segmented compressed sampling (CS) method for analog-to-information conversion (AIC) has been proposed in our recent work. Its essence is to collect a larger number of samples (although correlated) than the number of parallel branches of mixers and integrators in the AIC devise. The objective of this paper is to prove that the additional samples obtained based on the proposed segmented CS method lead to improved signal recovery quality. The study is performed based on the empirical risk minimization recovery method, but the least absolute shrinkage and selection operator algorithm can also be viewed as a particular realization of the empirical risk minimization method.