Image denoising algorithm in spatial domain

Image denoising algorithm in spatial domain

Image denoising you want to use redundant information from the image itself to remove the image noise without affecting the image details. But often both cannot be combined. The following mainly introduces three kinds of denoising algorithms based on Gaussian weighting in spatial domain, namely Gaussian filtering algorithm, bilateral filtering and non-local mean value filtering. The filters are analyzed in terms of filtering method, filtering performance and computational complexity.

Gaussian Filter Gaussian filter:

Gaussian filtering is based on the Gaussian weighting of the pixel distance between the neighbors to assign weights, the specific formula is as follows

Gaussian function

3D Gaussian kernel function

The Fourier transform of Ivigos function kernel can be found that Gaussian filter is a low-pass filter. When the Sigma value gradually becomes larger, the Gaussian Fourier transform frequency width becomes smaller, which is to filter out more high-frequency signals.

Filtering performance: The image Gaussian noise has a good filtering effect, but the image of the details of the larger damage.

Bilateral filter Bilateral filter:

On the basis of Gaussian filtering, the bilateral filtering can further modify the weighted weights based on the similarity between the pixel values of the image.

The weight calculation has two parts, respectively, according to the neighborhood pixel position difference computation weight, namely defines the domain kernel, this part is the Gaussian filter function core:

The weight computed based on the neighborhood pixel value difference, which is the domain core:

The final weight:

Filtering performance: Bilateral filtering to correct the Gaussian filter kernel by increasing the range kernel, to some extent, change the function core of the detail part, compared with the simple Gaussian filter algorithm, the bilateral filter can ensure the recognition and retention of the detail part on the basis of satisfying the noise removal.

Non-local mean filter nonlocal mean filter:

Non-local mean filtering is a kind of filtering method proposed by Buades in 2005. The basic idea is to calculate the weighting of neighborhood pixels based on the self-similarity of images.

NML algorithm first needs to select two windows, respectively, similar Windows and Search window, similar window is selected to compare the similarity of two pixels, the search window is chosen to determine the range of similar pixels to calculate. The similarity weights between the center pixel I and the pixel J of its neighborhood are determined by the Euclidean distance of the Gaussian weighting of the two-pixel-like window, the formula is as follows:

Compared with bilateral filtering, non-local mean filtering determines the similarity between two pixels according to the similarity between the image slices with a certain size, which can better identify the details of the image than the bilateral filter. But the non-local mean algorithm filter parameter H is difficult to adjust,H control attenuation speed, if not too large decay algorithm will degenerate to mean filter, too small attenuation algorithm will not smooth effect, general H The selection of parameters will refer to the standard deviation of the image noise.

Reference documents

Buadesa,coll B,morel J M. A review of Image denoising Algorithms,with a new one.

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Image denoising algorithm in spatial domain