# Block-matching and 3D filtering

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Block-matching and 3D filtering (BM3D) is a 3-D block-matching algorithm used primarily for noise reduction in images. [1]

## Method

### Grouping

Image fragments are grouped together based on similarity, but unlike standard k-means clustering and such cluster analysis methods, the image fragments are not necessarily disjoint. This block-matching algorithm is less computationally demanding and is useful later on in the aggregation step. Fragments do however have the same size. A fragment is grouped if its dissimilarity with a reference fragment falls below a specified threshold. This grouping technique is called block-matching, it is typically used to group similar groups across different frames of a digital video, BM3D on the other hand may group macroblocks within a single frame. All image fragments in a group are then stacked to form 3D cylinder-like shapes.

### Collaborative filtering

Filtering is done on every fragments group. A ${\displaystyle d+1}$[ clarification needed ] dimensional linear transform is applied, followed by a transform-domain shrinkage such as Wiener filtering, then the linear transform is inverted to reproduce all (filtered) fragments.

### Aggregation

The image is transformed back into its two-dimensional form. All overlapping image fragments are weight-averaged to ensures that they are filtered for noise yet retain their distinct signal.

## Extensions

### Color images

RGB images can be processed much like grayscale ones. A luminance-chrominance transformation should be applied to the RGB image. The grouping is then completed on the luminance channel which contains most of the useful information and a higher SNR. This approach works because the noise in the chrominance channels is strongly correlated to that of the luminance channel, and it saves approximately one-third of the computing time because grouping takes up approximately half of the required computing time.

### Deblurring

The BM3D algorithm has been extended (IDD-BM3D) to perform decoupled deblurring and denoising using the Nash equilibrium balance of the two objective functions. [2]

### Convolutional neural network

An approach that integrates a convolutional neural network has been proposed and shows better results (albeit with a slower runtime). [3] MATLAB code has been released for research purpose. [4]

## Related Research Articles

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## References

1. Dabov, Kostadin; Foi, Alessandro; Katkovnik, Vladimir; Egiazarian, Karen (16 July 2007). "Image denoising by sparse 3D transform-domain collaborative filtering". IEEE Transactions on Image Processing. 16 (8): 2080–2095. Bibcode:2007ITIP...16.2080D. CiteSeerX  . doi:10.1109/TIP.2007.901238.
2. Danielyan, Aram; Katkovnik, Vladimir; Egiazarian, Karen (30 June 2011). "BM3D Frames and Variational Image Deblurring". IEEE Transactions on Image Processing. 21 (4): 1715–28. arXiv:. Bibcode:2012ITIP...21.1715D. doi:10.1109/TIP.2011.2176954. PMID   22128008.
3. Ahn, Byeongyong; Ik Cho, Nam (3 April 2017). "Block-Matching Convolutional Neural Network for Image Denoising". arXiv: [Vision and Pattern Recognition Computer Vision and Pattern Recognition].
4. "BMCNN-ISPL". Seoul National University. Retrieved 3 January 2018.
5. "LASIP - Legal Notice". Tampere University of Technology (TUT). Retrieved 2 January 2018.
6. Lebrun, Marc (8 August 2012). "An Analysis and Implementation of the BM3D Image Denoising Method". Image Processing on Line. 2: 175–213. doi:.