Optimizing measurements for feature-specific compressive sensing

While the theory of compressive sensing has been very well investigated in the literature, comparatively little attention has been given to the issues that arise when compressive measurements are made in hardware. For instance, compressive measurements are always corrupted by detector noise. Further, the number of photons available is the same whether a conventional image is sensed or multiple coded measurements are made in the same interval of time. Thus it is essential that the effects of noise and the constraint on the number of photons must be taken into account in the analysis, design, and implementation of a compressive imager. In this paper, we present a methodology for designing a set of measurement kernels (or masks) that satisfy the photon constraint and are optimum for making measurements that minimize the reconstruction error in the presence of noise. Our approach finds the masks one at a time, by determining the vector that yields the best possible measurement for reducing the reconstruction error. The subspace represented by the optimized mask is removed from the signal space, and the process is repeated to find the next best measurement. Results of simulations are presented that show that the optimum masks always outperform reconstructions based on traditional feature measurements (such as principle components), and are also better than the conventional images in high noise conditions.