Image Noise Reduction via Geometric Multiscale Ridgelet Support Vector Transform and Dictionary Learning

Advances in machine learning technology have made efficient image denoising possible. In this paper, we propose a new ridgelet support vector machine (RSVM) for image noise reduction. Multiscale ridgelet support vector filter (MRSVF) is first deduced from RSVM, to produce a multiscale, multidirection, undecimated, dyadic, aliasing, and shift-invariant geometric multiscale ridgelet support vector transform (GMRSVT). Then, multiscale dictionaries are learned from examples to reduce noises existed in GMRSVT coefficients. Compared with the available approaches, the proposed method has the following characteristics. The proposed MRSVF can extract the salient features associated with the linear singularities of images. Consequently, GMRSVT can well approximate edges, contours and textures in images, and avoid ringing effects suffered from sampling in the multiscale decomposition of images. Sparse coding is explored for noise reduction via the learned multiscale and overcomplete dictionaries. Some experiments are taken on natural images, and the results show the efficiency of the proposed method.