`skimage.restoration._denoise:denoise_tv_bregman`

source: /dev/scikit-image/src/skimage/restoration/_denoise.py :282

Signature

   def     denoise_tv_bregman (    image    ,    weight    =  5.0   ,    max_num_iter    =  100   ,    eps    =  0.001   ,    isotropic    =  True   ,  * ,     channel_axis    =  None     )

Summary

Perform total variation denoising using split-Bregman optimization.

Extended Summary

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:

u min i = 0 \sum N - 1 (∣ \nabla u_{i} ∣ + \frac{λ}{2} (f_{i} - u_{i})^{2})

where $λ$ is a positive parameter. The first term of this cost function is the total variation; the second term represents data fidelity. As $λ \to 0$ , 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

image : ndarray: Input image to be denoised (converted using img_as_float).
weight : float, optional: Denoising weight. It is equal to $\frac{λ}{2}$ . Therefore, the smaller the weight, the more denoising (at the expense of less similarity to image).
eps : float, optional: Tolerance $ε > 0$ for the stop criterion: The algorithm stops when $∥ u_{n} - u_{n - 1} ∥_{2} < ε$ .
max_num_iter : int, optional: Maximal number of iterations used for the optimization.
isotropic : bool, optional: Switch between isotropic and anisotropic TV denoising.
channel_axis : int 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.
versionadded 0.19
channel_axis was added in 0.19.

Returns

u : ndarray: Denoised image.

Notes

Ensure that channel_axis parameter is set appropriately for color images.

The principle of total variation denoising is explained in ^[4]. It is about minimizing the total variation of an image, which can be roughly described as the integral of the norm of the image gradient. Total variation denoising tends to produce cartoon-like images, that is, piecewise-constant images.

Aliases

skimage.restoration.denoise_tv_bregman

Signature

Summary

Extended Summary

Parameters

Returns

Notes

See also

Aliases