Images are Easier to Restore than 1-D Signals: A Theoretical Explanation of a Surprising Empirical Phenomenon

Similar techniques are often used to restore 1-D signals and 2-D images from distorted (\blurred") observations. From the purely mathematical viewpoint, 1-D signals are simpler, so it should be easier to restore signals than images. However, in practice, it is often easier to restore a 2-D image than to restore a 1-D signal. In this paper, we provide a theoretical explanation for this surprising empirical phenomenon. c