Multiresolution pattern spectrum and its application to optimization of nonlinear filter

The optimization methods of nonlinear filters by supervised learning have been investigated. However, the optimized filter is still uncertain to be effective for images other than the example pair of a noisy image and its ideal output used for the optimization. In this paper, a novel optimization method by unsupervised learning using a novel definition of the pattern spectrum, named multiresolution pattern spectrum (MPS), is proposed. The pattern spectrum extracts the contribution of the figures in images to each size by mathematical morphology. The MPS can separate smaller portions and approximate shapes of larger portions. Our optimization method tunes the filter to reduce the portions of smaller sizes on MPS, since these are regarded as the contribution of noise. This method is free from the above problem of supervised learning methods since it uses only the target noisy image itself