Showing papers on "Harmonic wavelet transform published in 2021"

Image De-noising with a New Threshold Value Using Wavelets

Abstract: The image de-noising is the process to remove the noise from the image naturally corrupted by the noise. The wavelet method is one among the various methods for recovering infinite dimensional objects like curves, densities, images etc. The wavelet techniques are very effective to remove the noise because of its ability to capture the energy of a signal in few energy transform values. The wavelet methods are based on shrinking the wavelet coefficients in the wavelet domain. This paper concentrates on selecting a threshold for wavelet function estimation. A new threshold value is pro-posed to shrink the wavelet coefficients obtained by wavelet decomposition of a noisy image by considering that the sub band coefficients have a generalized Gaussian distribution. The proposed threshold value is based on the power of 2 in the size 2^J x 2^J of the data that can be computed efficiently. The experiment has been conducted on various test images to compare with the established threshold parameters. The result shows that the proposed threshold value removes the noise significantly.

Existence of Uncertainty Minimizers for the Continuous Wavelet Transform

Abstract: Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time-scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals.