Multiscale Optimal Filtering on the Sphere

Abstract

We present a framework for the optimal filtering of spherical signals contaminated by realizations of zero-mean anisotropic noise processes. Filtering is performed in the wavelet domain given by the scale-discretized wavelet transform on the sphere. The proposed filter is optimal in the sense that it minimizes the mean square error between the filtered wavelet representation and wavelet representation of the noise-free signal. We also present a simplified formulation of the filter for the case when azimuthally symmetric wavelet functions are used. We demonstrate the use of the proposed optimal filter for denoising of an Earth topography map in the presence of uncorrelated, zero-mean, White Gaussian noise. The proposed filter is found to be superior to the hard thresholding method, particularly in the high noise regime.

Method for Adaptive Wavelet Filtering of Speech Signals Based on Daubechies Filters with Minimization of Errors in Finding Optimal Thresholds

“…Classical methods for cleaning speech signals from noise and extracting the true waveform are Fourier analysis methods. However, their insufficient ability to localize signal singularities and the need to introduce data windows in the time domain with subsequent spectrum blurring limits the use of Fourier analysis algorithms and causes a reasonable movement of speech signal processing practice and theory towards methods that provide better frequency and time resolution [1].…”