Wavelet Basis Selection in Signal Denoising Based on Wavelet-Coefficient Distribution Shape

Denoising one-dimensional signals by wavelet shrinkage critically depends on the choice of wavelet basis, yet basis selection is often guided by heuristics rather than explicit statistical criteria. This paper investigates the relationship between wavelet-basis properties and the shape of the probability density function (PDF) of the detail coefficients in the coarsest retained detail subband. On this basis, it proposes the shape of this PDF as a criterion for wavelet-basis selection. We hypothesize that, for a fixed decomposition depth, noise model, and shrinkage rule, a basis better matched to the signal’s local regularity produces a narrower and more sharply peaked coefficient PDF in this subband than a mismatched basis and can therefore serve as a data-driven indicator for basis selection. To evaluate the consistency of this proposal, we perform controlled hard-thresholding experiments on six canonical test signals, five wavelet bases, and additive white Gaussian noise. Although the test signals differ significantly in local regularity and features, the relationship between basis suitability and PDF shape is confirmed for each of them. Therefore, the results suggest that the proposed PDF-shape criterion is a valuable indicator for wavelet-basis selection.