DEEP MORPHOLOGICAL FILTER NETWORKS FOR GAUSSIAN DENOISING

This paper presents a deep network based on morphological filters for Gaussian denoising. The opening and closing, which are basic morphological filters, can eliminate small peaks and valleys of intensities of images. Top-hat transforms are defined as subtractions between an original image and its opening or closing and extract peaks or valleys of the image. Each layer of the proposed network consists of top-hat transforms to attenuate peaks and valleys of noise components. Noise components are iteratively reduced in the proposed deep network structure. In this paper, the extensions of opening and closing are introduced by linear combinations of the morphological filters for the deep network. Multiplications are required for only the linear combination of the morphological filters in the proposed network. Since almost parameters of the network are structuring elements of the morphological filters, the feature maps and parameters can be represented in short bit-length integers. Denosing examples show the proposed network obtains denosing results comparable to BM3D without linear convolutions with the number of parameters that is about $1/10$ of full scale deep convolutional neural networks.