Optimal image alignment with random measurements

We consider the problem of image alignment using random measurements. More specifically, this paper is concerned with estimating a transformation that aligns a given reference image with a query image, assuming that not the images themselves but only random measurements are available. According to the theory behind compressed sensing, random projections of signal manifolds nearly preserve pairwise Euclidean distances when the reduced space is sufficiently large. This suggests that image alignment can be performed effectively based on a sufficient number of random measurements. We build on our previous work in order to show that the corresponding objective function can be decomposed as the difference of two convex functions (DC). Thus, the optimization problem becomes equivalent to a DC program that can be solved by an outer-approximation cutting plane method, which always converges to the globally optimal solution.