Translation- and direction-invariant denoising of 2D and 3D images: experience and algorithms
Thomas Yu, A. Stoschek, David L. Donoho · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
Removal of noise from 2D and 3D datasets is a task frequently needed in applications typical examples including in magnetic resonance imaging, in seismic exploration, and in video processing. We are currently interested in visualizing macromolecular structures of biological specimen, in which slices of very noisy electron microscopy (EM) images are volume rendered. Volume rendering of those datasets without any denoising normally gives very 'foggy' results that are not very informative. The wavelet and image processing communities have proposed in the past decade various multiscale image representations, many of which are of potential use for image de-noising. One of our goals here is to explore the importance of translation and direction invariance to the quality of reconstruction, which leads us to study the use of various tight frames for image reconstruction. We have developed 2D translation invariant transforms for both the isotropic and anisotropic wavelet bases. These allow us to develop a 2D analog of the 1D translation invariant de-noising algorithm proposed by Coifman and Donoho. We have also developed algorithms for implementing directionally-invariant de-noising for digital images. We have experiments to measure the relative importance of translation- and direction-invariance for both isotropic and anisotropic transforms. We also are exploring how to apply tight frames for linear inversion of noisy indirect data, which is what ultimately is needed in EM tomography.