The measurement performance of the baseline system design for the ITER high-frequency magnetic diagnostic system and attempts at its optimization have been performed using an innovative method based on the sparse representation of signals and the minimization of the maxima of the spectral window for integer mode numbers. This analysis has led to the conclusion that 350-500 sensors are in fact needed to satisfy the ITER requirements for the measurement performance and the risk management over the machine life-time, instead of the originally foreseen ~170 sensors. In part-1 of this paper we have presented the general summary results of our work; here we present a more complete overview of the analysis method and further details of our test calculations, as an accompanying paper in this same journal issue.