Mixed‐delay wavelet deconvolution of the point‐source seismogram

Wavelet deconvolution

This paper studies the issue of optimal deconvolution density estimation using wavelets. We explore the asymptotic properties of estimators based on thresholding of estimated wavelet coe cients. Minimax rates of convergence under the integrated square loss are studied over Besov classes B pq of functions for both ordinary smooth and supersmooth convolution kernels. The minimax rates of converge...

Deconvolution: a wavelet frame approach

This paper devotes to analyzing deconvolution algorithms based on wavelet frame approaches, which has already appeared in [6,8,9] as wavelet frame based high resolution image reconstruction methods. We first give a complete formulation of deconvolution in terms of multiresolution analysis and its approximation, which completes the formulation given in [6,8,9]. This formulation converts deconvol...

Filtering and deconvolution by the wavelet transform

The wavelet transform gives information in both spatial and frequency domains and is a very useful tool for describing the hierarchical structures. A new approach for filtering based on the wavelet transform is presented in this paper, and several algorithms are proposed . A criterion of quality, which takes into account the resolution, is used to compare these algorithms . We show that deconvo...

Wavelet-based Deconvolution for Ill-conditioned Systems Wavelet-based Deconvolution for Ill-conditioned Systems

This thesis proposes a new approach to wavelet-based image deconvolution that comprises Fourier-domain system inversion followed by wavelet-domain noise suppression. In contrast to other wavelet-based deconvolution approaches, the algorithm employs a regularized inverse lter, which allows it to operate even when the system is non-invertible. Using a mean-square-error metric, we strike an optima...

Wavelet Estimation via Sparse Multichannel Blind Deconvolution