This is the source code for "Minmax-concave Total Variation Denoising" (2D case).

Du, H. & Liu, Y. Minmax-concave Total Variation Denoising.

Signal, Image and Video Processing (2018).

doi: 10.1007/s11760-018-1248-2

url: https://link.springer.com/article/10.1007/s11760-018-1248-2

• Python 3
• numpy
• scipy
• skimage
• matplotlib

• For demonstration, you can simply clone the repository and run main.py. Denoising results as well as error images of three methods TV, NLTV and MCTV are plotted. Below is one demo figure.

• The demo 2D 256 × 256 synthetic block image and the corresponding noisy one are saved as image.mat and noi_image.mat, respectively. One thing I should point out is that the noisy image was generated by function imnoise in MATLAB. One reason I choose this function is that, after adding noise, it truncates outliers, and the pixel values stay within proper range (e.g., for gray image, the pixel range is [0, 1]).

• Feel free to explore and modify all parameter values in main.py. For detailed explanation of each parameter and its proper value range, please see the comment in code.

• For MATLAB version of the source code, you can email me: yilinl2@andrew.cmu.edu.

• I followed the instruction and used the source code of "Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction" to get the NLTV denoising result (paper url: https://doi.org/10.1137/090746379), and saved it as NLTV.jpg. It greatly facilitates my coding process. You may download the source code from the author Xiaoqun Zhang's homepage, or here: http://math.sjtu.edu.cn/faculty/xqzhang/html/code.html.

• For more algorithm details, please see tv2d.py and mctv2d.py or the relevant research paper.