skimage2.restoration.denoise_tv_bregman#

skimage2.restoration.denoise_tv_bregman(image, weight=5.0, max_num_iter=100, eps=0.001, isotropic=True, *, channel_axis=None)[source]#

Perform total variation denoising using split-Bregman optimization.

Given \(f\), a noisy image (input data), total variation denoising (also known as total variation regularization) aims to find an image \(u\) with less total variation than \(f\), under the constraint that \(u\) remain similar to \(f\). This can be expressed by the Rudin–Osher–Fatemi (ROF) minimization problem:

\[\min_{u} \sum_{i=0}^{N-1} \left( \left| \nabla{u_i} \right| + \frac{\lambda}{2}(f_i - u_i)^2 \right)\]

where \(\lambda\) is a positive parameter. The first term of this cost function is the total variation; the second term represents data fidelity. As \(\lambda \to 0\), the total variation term dominates, forcing the solution to have smaller total variation, at the expense of looking less like the input data.

This code is an implementation of the split Bregman algorithm of Goldstein and Osher to solve the ROF problem ([1], [2], [3]).

Parameters:

imagendarray: Input image to be denoised (converted using skimage2.util.img_as_float()).
weightfloat, optional: Denoising weight. It is equal to \(\frac{\lambda}{2}\). Therefore, the smaller the weight, the more denoising (at the expense of less similarity to image).
epsfloat, optional: Tolerance \(\varepsilon > 0\) for the stop criterion: The algorithm stops when \(\|u_n - u_{n-1}\|_2 < \varepsilon\).
max_num_iterint, optional: Maximal number of iterations used for the optimization.
isotropicbool, optional: Switch between isotropic and anisotropic TV denoising.
channel_axisint or None, optional: If None, the image is assumed to be grayscale (single-channel). Otherwise, this parameter indicates which axis of the array corresponds to channels.

Added in version 0.19: channel_axis was added in 0.19.

Returns:

undarray: Denoised image.