Multiresolution adaptive noise filtering based on Laplacian pyramids

A recently investigated approach to noise filtering in digital images consists of considering a multiresolution decomposition of the input image, and applying a different adaptive filter to each resolution layer. The wavelet decomposition has been employed for multiresolution noise- reduction, thanks to its capability to capture spatial features within frequency subbands. Conversely, Laplacian pyramids (LP) look attractive because of their full band- pass frequency property, which enables connected image structures to be represented on multiple scales. The idea of the present work is to apply an adaptive minimum mean squared error filter to the connectivity-preserving different resolution layers into which the noisy image is decomposed. For natural images, each layer of the LP is characterized by a signal-to-noise ratio (SNR) that decreases for increasing spatial resolution. Therefore, each filter may be tuned to the SNR of the related layer, so as to preserve the spatial details of the less noisy layers to a larger extent. Once all the resolutions, including the base-band, have been adaptively smoothed, a noise-filtered image version is achieved by recombining the layers of the LP. Theoretical frameworks are developed for both additive and multiplicative noise models. Experimental results of de- noising carried out on images with simulated noise and on true synthetic aperture radar images validate the potentiality of the approach in terms of both SNR improvement and visual quality