regularized restoration

Regularized restoration solves \hat{\mathbf x} = \arg\min_{\mathbf x}\left(\lVert H\mathbf x-\mathbf b\rVert^2 + \lambda R(\mathbf x)\right) for some penalty R(\mathbf x) and strength \lambda, generalizing the Wiener filter (R(\mathbf x)=\lVert\mathbf x\rVert^2, ridge regularization diagonalized per frequency) to a wider family that includes, e.g., total-variation regularization (Chapter 13). Too small a \lambda leaves noise unchecked; too large a \lambda smooths away real detail along with it.