ResPoND

A MATLAB package for the restoration of directional images corrupted by Poisson noise.

Authors

Daniela di Serafino, University of Naples Federico II, Napoli, Italy, daniela.diserafino[at]unina.it
Germana Landi, University of Bologna, Bologna, Italy, germana.landi[at]unibo.it
Marco Viola, University of Campania "Luigi Vanvitelli", Caserta, Italy, marco.viola[at]unicampania.it

Last Update

Version 1.1 - July 18, 2021

Description

ResPoND (Restoration of Poisson-Noisy Directional images) is a MATLAB package for deblurring directional images corrupted by Poisson noise.

The main function in the package, named respond, performs the restoration by minimizing the KL-DTGV_2 model presented in [1]. Given the noisy and blurry observed image b, the linear bluring operator A, the background noise gamma, and the regularization parameter lambda, the function finds an approximate solution to the nonsmooth constrained minimization problem

          min  lambda*KL(A*u + gamma, b) + DTGV_2(u)
          s.t. x >= 0,

where KL is the so-called Kullback-Leibler divergence of the blurred image A*u + gamma from the observed image b and DTGV_2 is the discrete second-order Total Generalized Variation regularization term. The minimization problem is solved by a specialized version of a two-block Alternating Direction Method of Multipliers (ADMM) (see Algorithm 2 in [1]).

The respond function is also suited for the deblurring of general Poissonian images by the minimization of the KL-TGV_2 model (see the function documentation for further details).

References

[1] D. di Serafino, G. Landi and M. Viola, Directional TGV-Based Image Restoration under Poisson Noise, Journal of Imaging, volume 7(6), 2021, p. 99, DOI: 10.3390/jimaging7060099 (open access).

Software requirements

ResPoND runs under MATLAB. It has been tested under MATLAB R2020a.

Contents of the package

Here is the list of ResPoND files:

respond.m : main function;
dir_est_hough.m : function estimating the main direction of directional images;
plot_line_rad.m : function plotting a line along a specified direction at the center of the current image.
ssim_index.m : implementation of the algorithm for calculating the Structural SIMilarity (SSIM) index between two images by Zhou Wang.

See the documentation inside each file for further details.

Example of use

DTGVdemo.m : example of use for the case of directional images;
fibre_phantom.mat : phantom directional image;
TGVdemo.m : example of use for the case of general images;
smooth_phantom.mat : phantom smooth image.

diserafi/respond