Efficient Signal Reconstruction for a Broad Range of Applications

The signal reconstruction problem (SRP) is an important optimization problem where the objective is to identify a solution to an under-determined system of linear equations AX = b that is closest to a given prior. It has a substantial number of applications in diverse areas including network traffic engineering, medical image reconstruction, acoustics, astronomy and many more. Most common approaches for solving SRP do not scale to large problem sizes. In this paper, we propose a dual formulation of this problem and show how adapting database techniques developed for scalable similarity joins provides a significant speedup when the A matrix is sparse and binary. Extensive experiments on real-world and synthetic data show that our approach produces a significant speedup of up to 20x over competing approaches.