Learning Moore-Penrose based residuals for robust non-blind image deconvolution

This work was supported by grants P20_00286 and B-TIC-324-UGR20 funded by Consejería de Universidad, Investigación e Innovación ( Junta de Andalucía ) and by “ ERDF A way of making Europe”. Funding for open access charge: Universidad de Granada / CBUA.This paper proposes a deep learning-based method for image restoration given an inaccurate knowledge of the degradation. We first show how the impulse response of a Wiener filter can approximate the Moore-Penrose pseudo-inverse of the blur convolution operator. The deconvolution problem is then cast as the learning of a residual in the null space of the blur kernel, which, when added to the Wiener restoration, will satisfy the image formation model. This approach is expected to make the network capable of dealing with different blurs since only residuals associated with the Wiener filter have to be learned. Artifacts caused by inaccuracies in the blur estimation and other image formation model inconsistencies are removed by a Dynamic Filter Network. The extensive experiments carried out on several synthetic and real image datasets assert the proposed method's performance and robustness and demonstrate the advantage of the proposed method over existing ones.Junta de Andalucía P20_00286, B-TIC-324-UGR20ERDF A way of making EuropeUniversidad de Granada / CBU

On the Comparisons of Decorrelation Approaches for Non-Gaussian Neutral Vector Variables

As a typical non-Gaussian vector variable, a neutral vector variable contains nonnegative elements only, and its l₁-norm equals one. In addition, its neutral properties make it significantly different from the commonly studied vector variables (e.g., the Gaussian vector variables). Due to the aforementioned properties, the conventionally applied linear transformation approaches [e.g., principal component analysis (PCA) and independent component analysis (ICA)] are not suitable for neutral vector variables, as PCA cannot transform a neutral vector variable, which is highly negatively correlated, into a set of mutually independent scalar variables and ICA cannot preserve the bounded property after transformation. In recent work, we proposed an efficient nonlinear transformation approach, i.e., the parallel nonlinear transformation (PNT), for decorrelating neutral vector variables. In this article, we extensively compare PNT with PCA and ICA through both theoretical analysis and experimental evaluations. The results of our investigations demonstrate the superiority of PNT for decorrelating the neutral vector variables