DSP2-Final Project:Different Optimization Method to Implement Total Variation Denoising

This project is aim to use different optimization method to do image denoising based on total variation denoising.

To run these codes, install numpy,matplotlib,scipy,PIL,skimage packages.
In this project, the original image is Lena512 which is often used in image processing. Add normal distributed noise to the image and do TVD denoising.

Packages used in project

The linear_operator.py and proximal_operator.py defines some function of processing data. Cost_function.py defines the function to calculate the cost of the model we choose in iamge processing.
denoise_tv_chambolle.py uses the chambolle method to do denoising.
denoise_tv_gradient.py is based on the gradient descent model, and I design this method only based on mathematical way and assume the image has constinuous value, this is an approximate method to do denoising.
denoise_tv_rof_primal_dual.py is based on primal-dual algorithm which is widely used in optimization. This method is based on rof model and it shows great ability to denoise normal distributed noise in image processing.
denoise_tv_fista.py is also based on primal_dual algorithrm and it use different optimization method to reach the optimal denoisd result. Usually it has fewer iterations to get covergence.

1.Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems. Amir Beck and Marc Teboulle
2.A Tutorial on Primal-Dual Algorithm. Shenlong Wang
3.ROF and TV-L1 denoising with Primal-Dual algorithm. Alexander Mordvintsev
4.An introduction to Total Variation for Image Analysis. Antonin Chambolle, Vicent Caselles, Matteo Novaga, Cremers, Thomas Pock, Daniel