Question

Found this very interesting code on total variation filter tvmfilter

The additional functions this code uses are very confusing but the denoising is far better than all the filters i have tried so far

i have figured out the code on my own 🙂

Answer 1

His additional function “tv” denoises with the ROF model which has been a major research topic for two decades now. See http://www.ipol.im/pub/algo/g_tv_denoising/ for a summary of current methods.

Briefly, the idea behind ROF is to approximate the given noisy image with a piecewise constant image by solving an optimization which penalizes the total variation (ie l1-norm of the gradient) of the image.

The reason this performs well is that the other denoising methods you are probably working with denoise by smoothing the image via convolution with a Gaussian (ie penalizing the l2-norm of the gradient (ie solving the heat equation on the image) ). While fast to compute, denoising by smoothing blurs edges and thus results in poor image quality. l1-norm optimization preserves edges.

It’s not clear how Guy solves the tv problem in that code you linked. He references the original ROF paper so it’s possible that he’s just using the original method (gradient descent) which is quite slow to converge. I suggest you give this code/paper a try: http://www.stanford.edu/~tagoldst/Tom_Goldstein/Split_Bregman.html as it’s probably faster than the .m file you are using.

Also, as was mentioned in the comments, you will get better denoising (ie higher SNR) using nonlocal means. However, it will take much longer for the nonlocal means algorithm to work as it requires that you search the entire image for similar patches and compute weights based on them.