Deconvolution with a Box

TL;DR

This paper demonstrates that perfect reconstruction of sparse signals from box convolution is achievable using convex optimization, providing a tight bound that matches the information theoretic limit for super-resolution tasks.

Contribution

The authors provide a direct proof improving the reconstruction bound for deconvolution with a box, establishing a tight limit that aligns with information theory.

Findings

Convex optimization enables perfect sparse signal reconstruction from box convolution.

The derived bound for reconstruction is tight and optimal.

The results improve upon previous bounds in super-resolution deconvolution.

Abstract

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.