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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 = ZK 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 Zk are replaced by [\hat{Y}_{k+1}]. The PSD for each scale is estimated as described in Section 3.3[link].2[link]. 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}].

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