M.Sc Thesis

M.Sc StudentRam Idan
SubjectWavelets for Graphs and their Deployment to Image
DepartmentDepartment of Electrical and Computer Engineering
Supervisors PROF. Israel Cohen
PROF. Shalom Raz
Full Thesis textFull thesis text - English Version


Multichannel seismic deconvolution is employed when the structure of the earth is estimated by transmitting an acoustic wave into the ground and measuring the reflected energy resulting from impedance discontinuities. The observed seismic data can be modeled as a convolution between a two-dimensional (2D) reflectivity section and a one-dimensional (1D) seismic pulse (wavelet), which have been further degraded by additive noise. Deconvolution is used to minimize the effect of the wavelet and produce an increased resolution estimate of the reflectivity, where closely spaced reflectors can be identified. In this thesis we propose two multichannel blind deconvolution algorithms for the restoration of 2D seismic data. Both algorithms are based on a 2D reflectivity prior model, and use iterative multichannel deconvolution procedures which deconvolve the seismic data, while taking into account the spatial dependency between neighboring traces. The first algorithm employs in each iteration a modified maximum posterior mode (MPM) algorithm which estimates a reflectivity column from the corresponding observed trace using the estimate of the preceding reflectivity column. The second algorithm takes into account estimates of both the preceding and subsequent columns in the estimation process. Both algorithms are applied to synthetic and real data and demonstrate better results compared to those obtained by a single-channel deconvolution method. Expectedly, the second algorithm which utilizes more information in the estimation process of each reflectivity column is shown to produce better results than the first algorithm.