Denoising by hard-thresholding in 3D transform domain with block-matching

Overcompleteness due to overlapping. After processing all $Z_{x_{R}\in X}$ , the produced local block-estimates , $\forall x_{R}\in X$ form, in general, an overcomplete representation of the estimated image due to an overlap between them.

Final estimate. The estimate of the true image is computed as a weighted average of the overlapping local block-estimates
where $\chi _{x_{m}}:X$ is the characteristic function of the square support of a block located at $x_{m}\in X$ .