Recommended resources for noise reduction
Signal denosing is a well-studied technique in signal processing. It first began using simple techniques such as filtering. In this approach, the emphasis is laid on designing filters which can perform denosing techniques in a fast and efficient manner.

Later, when wavelet theory was developed, some researchers used wavelets to denosing the signal. Essentially, we can apply thresholding techniques (soft or hard threshold) on the coefficients of the wavelets. On reconstruction using the dominant coefficients, one can denoise the signal.

In the early 2000s, sparsity-based techniques were introduced where the input signal is represented using an over complete dictionary. In the reconstruction step, sparsity inducing norms were used to extract only the dominant columns of the dictionary. Popular approaches include LASSO and total variation denosing.

Reference


Useful reference with MATLAB codes http://www.numerical-tours.com/matlab/