Statistical Multirate High-Resolution Signal Reconstruction Using the EMD-IT Based Denoising Approach

A Kizilkaya,A Ukte,M D Elbi

doi:10.13164/re.2015.0226

Abstract

The reconstruction problem of a high-resolution (HR) signal from a set of its noise-corrupted low-resolu- tion (LR) versions is considered. As a part of this problem, a hybrid method that consists of four operation units is proposed. The first unit applies noise reduction based on the empirical mode decomposition interval-thresholding to the noisy LR observations. In the second unit, estimates of zero-interpolated HR signals are obtained by performing up-sampling and then time shifting on each noise reduced LR signal. The third unit combines the zero-interpolated HR signals for attaining one HR signal. To eliminate the ripple effect, finally, median filtering is applied to the re- sulting reconstructed signal. As compared to the work that employs linear periodically time-varying Wiener filters, the proposed method does not require any correlation infor- mation about desired signal and LR observations. The validity of the proposed method is demonstrated by several simulation examples.

Highlights

Multirate statistical signal processing have found great interest over the last two decades for coping with the problems such as spectrum estimation, prediction, sensor fusion, time-delay estimation, and reconstruction or estimation of a stationary random process from multiple observations measured at different sampling rates [1]
Using the least-squares (LS) approach, in [4], three optimal filter structures are proposed for the estimation of the HR random process from two observations, one of which is measured at full-rate with a low signal-to-noise ratio (SNR) and the other is measured at arbitrary low-rate with a high SNR
A generalized version of [3] is considered in [5] that is a preliminary work of dissertation presented in [6] where optimal multirate filtering procedure is formulated taking the second-order statistics into consideration for the goal of estimating an HR signal from LR measurements observed at different sampling rates

Summary

Introduction

Multirate statistical signal processing have found great interest over the last two decades for coping with the problems such as spectrum estimation, prediction, sensor fusion, time-delay estimation, and reconstruction or estimation of a stationary random process from multiple observations measured at different sampling rates [1]. Within the scope of the reconstruction or estimation of a WSS random signal through its noisy LR measurements observed at different sampling rates, studies that employ the optimal linear filtering referred as Wiener filtering are carried out under the guidance of Therrien [3,4,5,6,7,8,9]. A generalized version of [3] is considered in [5] that is a preliminary work of dissertation presented in [6] where optimal multirate filtering procedure is formulated taking the second-order statistics into consideration for the goal of estimating an HR signal from LR measurements observed at different sampling rates. It is remarked that both ME and Wiener filter based methods require the knowledge of second-order statistics related to the desired HR signal and the noisy LR observations

Objectives

Methods

Results

Conclusion