Dhruv Shah 1 †, Alankar Kotwal 2 † and Ajit Rajwade 3
† Equal Contribution
1 Department of Electrical Engineering, Indian Institute of Technology Bombay
2 The Robotics Institute, Carnegie Mellon University
3 Department of Computer Science & Engineering, Indian Institute of Technology Bombay
IEEE Global Conference on Signal and Information Processing 2018
Most existing work in design of sensing matrices for compressive recovery is based on optimizing some quality factor, such as mutual coherence, average coherence or the restricted isometry constant (RIC), of the sensing matrix. In this paper, we report anomalous results that show that such a design is not always guaranteed to yield better reconstruction results. We also present a method of matrix design based on the minimum mean squared error (MMSE) criterion, imposing statistical priors on signal and noise, and show that it yields results superior to results from coherence-based methods while taking into account physical constraints on the sensing matrix.
In this work, we present
- An average coherence-based design scheme for the chosen architecture and report anomalous behavior in mutual coherence and RIC values of designed matrices. This is an interesting negative result.
- A novel approach to sensing matrix design, using Bayesian A-optimality within the SCS framework subject to a learned GMM prior on natural image patches and optical constraints levied by the acquisition model.
- A comparison between random matrices and matrices designed with the above methods on a wide variety of natural images, showing the superiority of the latter approach