Table of Contents
The project aims to exploit Partial Differential Equations (PDEs) to solve Inverse Problem in Image Denoising. There are other approaches dealing with Inverse Problem, resumed in Figure below.
In theory, we are looking for a solution 
by minimizing the following cost:
with 
where 
is a set of possible solutions whose element values corresponding {0,...,255} for RGB images.
The 
term represents the consistency between the observation 
and and the solution 
, while the 
term is the regulator which depicts an expected property for the solution. In the project, we will expect to study the impact of different
regularization terms.
Data Term
The data term considered here is the norm 2 of difference between the solution and the observation ,
which is integrated through the image's spatial information 
.
Regulation Term
1. Heat Equation (HE)
Considering the prior term (or regularization) as the diffusion term in Heat Equation.
Minimizing the total energy E(u,v) by applying the gradient descent algorithm:
Diffusion Equation
where 
is the weighting factor, 
is the gradient step.
2. Total Variation (TV)
Recall the 
, the the diffusion equation will be:
3. Perona-Malik Diffusion (PM)
with different choices for function 
: 
, 
, 
.
Distributed under the MIT License. See LICENSE for more information.
Khoa NGUYEN - @v18nguyen - [email protected]
Project Link: https://github.com/v18nguye/IDwPDEs