Optimised Sparse Image Reconstruction via Densification and Relocation

We propose a novel data optimisation technique for sparse image reconstruction, which is useful for image compression and adaptive signal processing. Due to its nonconvexity, the optimisation problem for sparse image reconstruction is challenging. The proposed method relies on a simple-to-use framework applicable to numerous linear image reconstruction operators, such as splines and linear partial differential equation (PDE)-based inpainting. Our approach convincingly outperforms several established algorithms in terms of reconstruction quality and efficiency, thanks to a combinatorial optimisation for the initial guess and a continuous optimisation for further improvements. Moreover, we present a comparison among a set of highly competitive methods for image reconstruction. To our knowledge, this set of methods has not been thoroughly compared with optimised data previously. MSC: 65K10, 65D07, 90C59