Filtered wavelet thresholding methods. (Q1426753)

The quality of a denoised image depends on several factors, including especially the choice of the thresholding parameter \(\lambda\) and the use of a suitable filter function. In this paper the authors study a piecewise quadratic function of \(\lambda\) and an exponential function of \(\lambda\) that can be satisfyingly used as filters instead of the soft thresholding filter \textit{D. L. Donoho} and \textit{I. M. Johnstone} [Biometrika 81, No.~3, 425--455 (1994; Zbl 0815.62019)] commonly considered, and prove that the filtered approximation they obtain is a near-minimizer of the related functional. An analysis of several numerical experiments on test images, supporting the validity of the approach, is also included.