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Determining Decomposition Levels for Wavelet Denoising Using Sparsity Plot
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DOI：10.1109/ACCESS.2021.3103497.png)
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Abstract
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We present a method to select decomposition levels for noise thresholding in wavelet denoising. It is essential to determine the accurate decomposition levels to avoid inadequate noise reduction and/or signal distortion by noise thresholding. We introduce the concept of sparsity plot that captures the abrupt transition from noisy to noise-free Detail component, readily revealing the cut-off for the maximum decomposition levels. The method uses the sparsity parameter to determine the noise presence in each detail component and measures the magnitude change in the sparsity values to distinguish between noisy and noise-free Detail components. The method is tested on both model and experimental signals, and proves effective for various signal lengths and types, as well as different Signal-to-Noise Ratios (SNRs). The method can be embedded with any wavelet denoising method to improve its performance. The code is available via GitHub and denoising.cornell.edu, as well as the corresponding author's group website (http://signalsciencelab.com).
Keywords:
Noise measurement
Noise reduction
Indexes
Signal to noise ratio
Mathematical model
Wavelet transforms
Thresholding (Imaging)
Decomposition level selection
detail components
noise reduction
noise filtering
signal denoising
sparsity
wavelet denoising
wavelet transform
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