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One-dimensional real-time signal denoising using wavelet-based kalman filtering

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2007
Durmaz, Murat
Denoising signals is an important task of digital signal processing. Many linear and non-linear methods for signal denoising have been developed. Wavelet based denoising is the most famous nonlinear denoising method lately. In the linear case, Kalman filter is famous for its easy implementation and real-time nature. Wavelet- Kalman filter developed lately is an important improvement over Kalman filter, in which the Kalman filter operates in the wavelet domain, filtering the wavelet coeffi- cients, and resulting in the filtered wavelet transform of the signal in real-time. The real-time filtering and multiresolution representation is a powerful feature for many real world applications. This study explains in detail the derivation and implementation of Real-Time Wavelet-Kalman Filter method to remove noise from signals in real-time. The filter is enhanced to use different wavelet types than the Haar wavelet, and also it is improved to operate on higer block sizes than two. Wavelet shrinkage is integrated to the filter and it is shown that by utilizing this integration more noise suppression is obtainable. A user friendly application is developed to import, filter and export signals in Java programming language. And finally, the applicability of the proposed method to suppress noise from seismic waves coming from eartquakes and to enhance spontaneous potentials measured from groundwater wells is also shown.