Image Estimation From Projective Measurements Using Low Dimensional Manifolds

We look at the design of projective measurements based upon image priors. If one assumes that image patches from natural imagery can be modeled as a low rank manifold, we develop an optimality criterion for a measurement matrix based upon separating the canonical elements of the manifold prior. Any sparse image reconstruction algorithm has improved performance using the developed measurement matrix over using random projections. We implement a 2-way clustering then K-means algorithm to separate the estimated image space into low dimensional clusters for image reconstruction via a minimum mean square error estimator. Some insights into the empirical estimation of the image patch manifold are developed and several results are presented.