Optimal Adaptive Nonparametric Denoising of Multidimensional - Time Signal

TL;DR

This paper introduces an adaptive nonparametric method for denoising multidimensional time signals using Legendre expansion, achieving asymptotic optimality and improved accuracy over classical methods in both simulated and real data.

Contribution

It presents a novel adaptive denoising technique based on Legendre expansion with confidence regions, outperforming traditional kernel and wavelet methods.

Findings

Proposed method achieves higher precision in signal estimation.

Method successfully applied to seismic and image data.

Adaptive truncation useful for signal and image compression.

Abstract

We construct an adaptive asymptotically optimal in the classical norm of the space L(2) of square integrable functions non - parametrical multidimensional time defined signal regaining (adaptive filtration, noise canceller) on the background noise via multidimensional truncated Legendre expansion and optimal experience design. The two - dimensional case is known as a picture processing, picture analysis or image processing. We offer a two version of an confidence region building, also adaptive. Our estimates proposed by us have successfully passed experimental tests on problem by simulate of modeled with the use of pseudo-random numbers as well as on real data (of seismic signals etc.) for which our estimations of the different signals were compared with classical estimates obtained by the kernel or wavelets estimations method. The precision of proposed here estimations is better. Our adaptive truncation may be used also for the signal and image compression.