DATA-DRIVEN ALGORITHMS FOR GAUSSIAN MEASUREMENT MATRIX DESIGN IN COMPRESSIVE SENSING

In this paper, we provide two data-driven algorithms for learning compressive sensing measurement matrices with Gaussian entries. In contrast to the ubiquitous i.i.d. Gaussian design, we associate different variances with different signal entries, so that we may utilize training data to focus more energy on the ``most important'' parts of the signal. Our first algorithm is based on simple variance-proportional sampling (i.e., place more energy at locations where the signal tends to vary more), and our second overcomes limitations of the first by iteratively up-weighing and down-weighing the variance values according to reconstructions performed on the training signals. Our algorithms enjoy the advantages of being simple and versatile, in the sense of being compatible a diverse range of signal priors and/or decoding rules. We experimentally demonstrate the effectiveness of our algorithms under both generative priors with gradient-based recovery and sparse priors with l1-minimization based recovery.