An Adaptive Sparse Coding Algorithm for Efficient Reconstruction and Denoising of High-Dimensional Signals

Abstract

The process of reconstruction and denoising of high-dimensional signals is still one of the basic issues of contemporary signal processing because it is corrupted by noise, computationally expensive, and requires precise sparse representations. Traditional sparse coding methods like LASSO, OMP, and K-SVD typically use constant regularization parameters and sluggishly converge, which means they do not suit dynamically changing and noisy systems. In order to overcome these drawbacks, this paper suggests an Adaptive Sparse Coding Algorithm (ASCA) which combines in a unified algorithm adaptive dictionary learning and dynamic sparsity control. The proposed method proposes a data-driven regularization, which modulates the sparsity constraints according to the signal and residual error, making it possible to achieve higher accuracy in representation and to converge much quicker. Extensive tests on both synthetic and real-world high-dimensional data have shown that ASCA has better performance than traditional algorithms, with large gains in Peak Signal-to-Noise Ratio (PSNR), low Mean squared Error (MSE), and computational efficiency. The findings underline the strength and scalability of the suggested algorithm to achieve effective signal re-construction and denoising. On the whole, the ASCA system shows a bright prospect of being used in the next-generation signal processing in biomedical analysis, image restoration, and communication systems.