Denoising of electron tomographic reconstructions from biological specimens using multidimensional multiscale transforms

In electron tomographic reconstructions of biological specimens the information about their structure is not directly, accessible since most of the signal is buried in noise. An interpretation of the images using surface and volume rendering techniques is difficult due to the noise sensitivity of rendering algorithms. We explore the use of various multiscale representations for denoising 2D and 3D images. Orthogonal wavelet transforms applied to multidimensional data exhibit poor results due to the lack of translational and directional invariance. Extending the 1D translation-invariant denoising algorithm of Coifman and Donoho (see Technical Report no.475, Department of Statistics, Stanford University, 1995) to higher dimensions overcomes the poor performance of orthogonal wavelet transforms. We present a method to quantify the loss of information due to denoising artifacts on data with an unknown signal-noise relationship, and propose a scheme for denoising of such data. Experiments show that invariant wavelet denoising perform well in reconstructing signals from noisy 3D data while preserving most of the actual information.