Thresholding-based Wavelet Packet Methods for Doppler Ultrasound Signal Denoising
Doppler ultrasound is widely used to diagnose vascular diseases because of its noninvasive advantages. Denoising of Doppler signals is necessary as a pre-processing for a high quality Doppler ultrasound system. Recently, there has been much work on denois
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This paper presents a threshold-based wavelet packet denoising method, which preserves useful high frequency components and offers higher signal–to-noise ratio (SNR) compared with straightforward waveletbased denoising methods. We then propose several algorithms to improve the selection of the threshold, and these methods are adaptive in the sense of coefficients obtained from different decomposed levels using the characteristics of the wavelet transform. In computer simulations, we have tested our algorithms and show improved SNR of simulated Doppler I/Q signals and better visualization of displayed Doppler spectrum. Keywords — Doppler signal, threshold shrinkage denoising
wavelet
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I. INTRODUCTION Doppler ultrasound technology has been widely used in the clinic to diagnose vascular diseases, but the noise in Doppler systems deteriorates the quality of detected spectrum and velocity waveforms. Recently, there has been much work on denoising methods based on noise statistics and the spectrum distribution. Methods based on Fourier transform have less success because the frequency band of the signal is always overlapped with that of the noise. Methods based on wavelet transform, however, have comparatively satisfying results because the wavelet analysis offer better time-frequency analysis compared with Fourier analysis. Currently, the most extensively used waveletbased denoising methods, for example, the wavelet shrinkage denoising, can be seen as optimized approximation under least mean square error (MSE).
The wavelet decomposing method is suitable for signals with useful low frequency components, but may result in problems for signals with meaningful high frequency contents because it may treat them as noise and denoise them. In this paper we present a threshold-based wavelet packet denoising method where two threshold functions have been proposed to account for the pros and cons of the standard hard and soft thresholding functions. Section II describes the mathematical modeling of the ultrasound Doppler signals used in computer simulation. Wavelet packet analysis and thresholding has been introduced in Section III where we present our improved thresholding functions. Simulation results and analysis are discussed in Section IV. II. MATHEMATIC MODELING OF THE DOPPLER SIGNALS The detection of blood flow with ultrasound depends on the Doppler principle which determines that, when ultrasound is reflected from a moving structure, the frequency of the reflected waves is different from that of the incident waves. Besides the flow, other tissues such as vascular wall and cardiac muscle also reflect ultrasound wave. But the signal reflected by vascular wall and cardiac muscle are much stronger than that of flow. It is necessary to remove them, or called clutter, to extract useful flow signals. To investigate the performance of our denoising method, it’s necessary to have computer simulations of Doppler signals with varying mean blood frequencies plus clutter components, see Bjarum et.al [1]. Both the clut
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