Joint near-isometry and optimal sparse recovery: Nonuniform recovery from multi-sensor measurements

Abstract

Parallel acquisition systems are widely used in practical applications as they are effective in problems that cannot guarantee the quality of signal reconstruction in case of using a single-sensor system. Many authors have already demonstrated the superiority of the multi-sensor system over the single-sensor system by revealing the nonuniform recovery conditions of the multi-sensor system for optimal recovery in the sense that the number of measurements required per sensor decreases linearly with the total number of sensors, however, the condition on the sensor profile matrices are quite stringent. In this paper, we present nonuniform recovery guarantees based on the so-called joint near-isometry condition, while preserving the advantage of the multi-sensor system and the possibility of stable and robust recovery. The relaxed condition on the sensor profile matrices opens up the possibility of design of considerably wide range of sensor profile. On the other hand, numerical experiments not only show the validity of our theoretical result, but also provide several interesting results such as effectiveness of random sensor profile.