Frequency-domain blind deconvolution based on negentropy using standard symmetric power distribution

In this paper, a family of distributions, standard symmetric power distribution (SSPD), which would be proper to describe the seismic reflection coefficient is proposed. Special cases of this family include the triangular distribution, the standard power function distribution, and the uniform distribution. Properties of the distribution are investigated and the moment and entropy estimation is discussed. The two parameter distribution is investigated in the seismic reflection coefficient and the seismic record. And then the deconvolution method based on negentropy is developed using SSPD. The method works in the frequency domain and requires estimation of the signal's probability density function. Thus, the algorithm uses higher order statistics (except for Gaussian source) and allows non-minimum-phase filter estimation. In practice, a gradient based regularization term for limiting noise amplification is contained in the criterion, which can improve the anti-noise property and the continuity between the adjacent traces of the multichannel seismic record. The gradient function which represents a key point of this algorithm is simplified based on the introduction of SSPD. Finally, experiments point to the relevance of the proposed algorithm: 1) Any filter, minimum phase or not, can be estimated; 2) Based on the SSPD, we can calculate the entropy instead of its asymptotic value and as there is no need to estimate the parameter in this method, it has a good computing speed. 3) The introduction of the gradient regularization term can provide good results with a better performance of the anti-noise property and the continuity between the adjacent traces. Applications of the introduced method to both synthetic and real data show that the proposed method can expand the frequency band of the seismic data with small samples, fast computing speed, good anti-noise quality and continuity between the adjacent traces.