Signal Restoration with Fractional Transform Sparse Representation and Autoencoder

Signa1 denoising is a crucial task in image processing, audio analysis, and communications. Traditional methods often struggle to strike a balance between reducing noise and preserving important signal details. Existing methods exploit the potential of fractional transforms combined with sparse representation techniques. However, these approaches face challenges in achieving the desired balance due to limited sensitivity to signal variations, high computational complexity, restricted adaptability to diverse noise types, and the need for careful selection of transform parameters. To overcome these limitations, we propose a novel method called Fractional Transform Sparse Representation Denoising (FTSRD), which integrates fractional wavelet transform (FWT), fractional DCT (FDCT), sparse representation, and Deep Denoising Autoencoder (DDAE) techniques. The integration of DDAE in FTSRD provides several advantages. DDAE, being a deep learning-based model, has the capability to learn complex noise patterns and extract meaningful signal features. Experimental evaluations were conducted on synthetic signals and ECG signals. The results demonstrate the superior performance of FTSRD in reducing noise while preserving essential structural details. It also surpasses traditional methods in subjective and objective quality measures. In conclusion, FTSRD addresses the challenges associated with noise reduction and signal detail preservation, making it a valuable tool in various denoising applications.