A Fast Rank reduction Algorithm Based on Block Hankel Hankel Block Matrix vector Multiplication with Applications to Seismic Signal Processing

Abstract:

Cadzow filtering is a well known denoising technique in the seismic signal processing. This method first transforms the data measured in seismic remote sensing into a complex Block Hankel Hankel Block (BHHB) matrix， then it reduces the noise via singular value decomposition (SVD). Usually, the structure of BHHB matrix is ignored in the SVD computation， so that the computational time and memory storage are high especially when the size of matrix is large. This paper presents a fast and stable SVD algorithm for complex BHHB matrices. The fast SVD algorithm consists of two stages: Lanczos bidiagonalization (or tridiagonalization for symmetric BHHB matrix) and diagonalization using twisted factorization. By exploiting the structure of BHHB matrix, the SVD can be accelerated by a fast matrix vector multiplication based on the 1 D Fast Fourier Transform(FFT). Compared to the multi dimensional FFT implementation, the proposed method requires much less memory with the similar computational cost. Numerical experiments support this claim. Finally, the fast SVD method is applied to some seismic examples with the Cadzow filtering technique to reduce noises. It turns out that the proposed method is better than the prediction filtering and it is cost efficient in the speed and memory usage in seismic data processing, especially for large problems.