Double Least-Squares Projections Method for Signal Estimation

Abstract

A real-world signal is always corrupted with noise. The separation between a signal and noise is an indispensable step in a variety of signal-analysis applications across different scientific domains. In this paper, we propose a double least-squares projections (DLSPs) method to estimate a signal from the noisy data. The first least-squares projection is to find a signal-dimensional optimal approximation of the noisy data in the least-squares sense. In this step, a rough estimation of the signal is obtained. The second least-squares projection is to find an approximation of a signal in another crossed signal-dimensional space in the least-squares sense. In this step, a much improved signal estimation that is close to orthogonal to the separated noise subspace can be obtained. The DLSP implements projection operation twice to obtain an almost perfect estimation of a signal. The application of the DLSP method in seismic random noise attenuation and signal reconstruction demonstrates the successful performance in seismic data processing.