Algorithm 1: The training part of the soft compression algorithm for gray image.

Input:W images with size $M\times N$ Output: The codebook for the shape layer and detail layer Preprocess: predictive coding, negative-to-positive mapping and layer separation forZ← 1 to W do do    for matrx size $(u,v)$←$1\times 1$to$m\times n$, image coordinate $(i,j)$←$1\times 1$to$M\times N$ do      if $I_S^{\prime }[i,j:i+u,j+v]$ satisfies (48) and (49) then         Get the shape $S:=I_S^{\prime }[i,j:i+u,j+v]$         if S in the codebook then           Update the frequency of S in the codebook         else           Add S to the codebook         end if      end if    end for    Remove low-weight shapes based on frequency and size    Count the distribution of pixel values in the detail layer $I_D^{\prime }$ end for Generate the codebooks