ETV is a Github repository that provides MATLAB demos of two algorithms described in the paper "Enhanced total variation minimization for stable image reconstruction" by Congpei An, Hao-Ning Wu, and Xiaoming Yuan. The software demonstrates Algorithm 1 for image denoising and Algorithm 2 for image reconstruction in this paper, which can be accessed at this link.

Demo 1: Image Denoising

The demo_denoising.m script reproduces Figure 1 from the paper, showcasing the denoising capability of the enhanced TV model. It utilizes two functions:

• denoiseTV.m: This function solves the TV denoising model using the split Bregman method.
• denoiseETV.m: This function solves the enhanced TV denoising model using the DCA+ADMM approach (Algorithm 1 in the paper).

Demo 2: Image Reconstruction

The demo_reconstruction.m script reproduces the third column of Figure 5 in the paper, illustrating the reconstruction capability of the enhanced TV model. Additionally, a lightweight version of the demo, demo_reconstruction_lightweight.m, is provided, which focuses on reconstructing a 64-by-64 image.

Four functions are involved in the reconstruction demos:

• MRITV.m: This function solves the TV reconstruction model using the split Bregman method.
• MRIL12.m: This function solves the weighted anisotropic and isotropic TV reconstruction model using the DCA+split Bregman approach.
• MRIETV.m: This function solves the anisotropic enhanced TV reconstruction model using the DCA+ADMM approach (Algorithm 2 in the paper).
• MRIETVisotropic.m: This function solves the isotropic enhanced TV reconstruction model using the DCA+ADMM approach.

Handling Noisy Measurements

In situations where the measurements are noisy, with a noise level denoted as $\tau$, our Algorithm 2 requires a projection onto a ball centered at 0 with a radius of $\tau$. To implement this projection, the function project_L2.m from The Proximity Operator Repository needs to be utilized.