An MLP Neural Net with L1 and L2 Regularizers for Real Conditions of Deblurring

Abstract

Real conditions of deblurring involve a spatially nonlinear process since the borders are truncated, causing significant artifacts in the restored results. Typically, it is assumed to have boundary conditions to reduce ringing; in contrast, this paper proposes a restoration method which simply deals with null borders. We minimize a deterministic regularized function in a Multilayer Perceptron (MLP) with no training and follow a back-propagation algorithm with the L1 and L2 norm-based regularizers. As a result, the truncated borders are regenerated while adapting the center of the image to the optimum linear solution. We report experimental results showing the good performance of our approach in a real model without borders. Even if using boundary conditions, the quality of restoration is comparable to other recent researches.

Boundary reconstruction process of a TV-based neural net without prior conditions

“…In recent studies [9,10], we have developed an algorithm using a multilayer perceptron (MLP) to restore a real image without relying on the typical BCs of the literature. The main goal is to model the blurred image as truncation of the convolution operator, where the boundaries have been removed and they are not further used in the algorithm.…”

“…However, the success of the total variation (TV) in deconvolution [16][17][18][19][20] motivated its incorporation in the MLP. By means of matrix algebra and the approximation of the TV operator with the majorization-minimization (MM) algorithm of [19], we presented a newer version of the MLP [10] for both l 1 and l 2 regularizers and mainly devoted to compare the truncation model with the traditional BCs. Now we will analyze the TV-based MLP with the purpose of going into the boundary restoration process.…”

“…In this article, we present a simple solution to solve the TV-based solution by means of an MLP with back-propagation. Previous researches of the authors [10] showed that the MLP also using the 2 term of (9).…”

“…Taking advantage of the quadratic properties of the expression (25) and applying Matrix Calculus basis (see a detailed computation in [10]), the differentiation ∂E(m) ∂z (m) leads to…”

“…In our previous article [10], we adjusted l with solutions coming from the Bayesian state-of-art. However, we still need to investigate a particular algorithm for the MLP since those Bayesian approaches work only for circulant degradation models, but not for the truncated image of this article.…”