Deconvolution with a Box
This addresses a key operation for super-resolution in imaging, but it is incremental as it improves on previous bounds.
The paper tackled the problem of deconvolution with a box for super-resolution in pixel-shift cameras, achieving perfect reconstructions of sparse signals using convex optimization and proving a tight bound that matches an information theoretic limit.
Deconvolution with a box (square wave) is a key operation for super-resolution with pixel-shift cameras. In general convolution with a box is not invertible. However, we can obtain perfect reconstructions of sparse signals using convex optimization. We give a direct proof that improves on the reconstruction bound that follows from previous results. We also show our bound is tight and matches an information theoretic limit.