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] It is one of the expansions of the non-local means methodology.[2] There are two cascades in BM3D: a hard-thresholding and a Wiener filter stage, both involving the following parts: grouping, collaborative filtering, and aggregation. This algorithm depends on an augmented representation in the transformation site.[3]
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 [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 ensure that they are filtered for noise yet retain their distinct signal.