Ring artifact reduction via multiscale nonlocal collaborative filtering of spatially correlated noise

Mäkinen, Y.; Marchesini, S.; Foi, A.

doi:10.1107/S1600577521001910

Figure 5
Flowchart of the multiscale denoising process, starting from the noisy sinogram Z and resulting in the estimate $[\hat{Y}]$ of the streak-free sinogram, both of size n×m. First, Z is vertically rescaled into a sinogram Z₀ of size $[{n\!\times\!m_{{\rm v}}}]$ , $[{m_{{\rm v}}\!\le m}]$ , through the binning operator $[{\cal B}_{{\rm v}}]$ . Then, by repeated horizontal binning $[{\cal B}_{{\rm h}}]$ , Z₀ is progressively downscaled into a series of sinograms $[{Z_{k}\! = \!{\cal B}_{\rm h}\left(Z_{k-1}\right)}]$ , $[{k\! = \!1,\ldots,K}]$ , each of size $[\lceil 2^{-k}n\rceil\!\times\!m_{{\rm v}}]$ . The coarsest scale noisy input Z^*_K = Z_K is denoised with BM3D to produce $[\hat{Y}_{K}]$ . Then, recursively for $[{k\! = \!{K\!-\!1},\ldots,0}]$ , the noisy input $[{Z^{\,*}_{k}\! = \!Z_{k}-{\cal B}_{\rm h}^{\,-1}\!\left(Z_{k+1}\!-\!\hat{Y}_{k+ 1}\right)}]$ is denoised by BM3D to produce $[\hat{Y}_{k}]$ ; this definition of Z^*_k means that the coarse-scale horizontal components of Z_k are replaced by $[\hat{Y}_{k+1}]$ . The PSD for each scale is estimated as described in Section 3.3

. The resulting estimate $[\hat{Y}_{0}]$ of the horizontal debinning (size $[{n\!\times\!m_{{\rm v}}}]$ ) similarly replaces the coarse-scale vertical components of Z to obtain the full-size estimate $[\hat{Y}]$ .

JOURNAL OF
SYNCHROTRON
RADIATION

ISSN: 1600-5775

Volume 28| Part 3| May 2021| Pages 876-888

https://doi.org/10.1107/S1600577521001910

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