Wavelet Denoising Parameter Selection Method Based on Generalized Cross-Validation(GCV)

The wavelet threshold denoising method is fast and straightforward, widely applicable in various signal denoising scenarios. One of its critical aspects is the selection of the optimal wavelet basis and the determination of the best decomposition level. Addressing the challenge of unifying the wavelet basis and decomposition level when applying wavelet threshold denoising to noisy signals, a method based on the Generalized Cross-Validation (GCV) criterion for selecting optimal parameters is proposed. This algorithm defines an objective function based on the GCV criterion, aiming to minimize it to select the asymptotically optimal wavelet basis and the best decomposition level. To validate the rationale and effectiveness of this approach and to enhance the credibility and reliability of experimental results, we employ both hard thresholding (H) and soft thresholding (S) methods to handle different noisy signals. Furthermore, we evaluate the algorithm's performance using signal-to-noise ratio (SNR) and mean square error (MSE). Experimental results demonstrate that this method can rapidly and accurately identify the optimal combination of wavelet basis and decomposition level. Applying this combination to wavelet threshold denoising yields higher SNR and lower MSE.