# Recommended resources for noise reduction

I know the question What Resources Are Recommended for an Introduction to Signal Processing (DSP)? and I have already read some general DSP books, such as Rick Lyons's "Understanding DSP," and also have browsed through Oppenheim's.

More specifically, what (printed) book would you recommend for denoising techniques in general?

Including techniques adapted for audio, spectral subtraction, Wiener filtering, etc. and if possible adapted to discrete signal processing with an algorithm/engineering point of view (i.e. rather x[k] than continuous x(t) and integrals...)

I just ordered a used version of Advanced digital signal processing and noise reduction, Vaseghi, but I'm looking for other recommendations.

## 2 Answers

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

“Adaptive Filter Theory” by Simon Haykin is a classic text for all things adaptive filtering/noise reduction. The text is pretty heavy on math, but I think if you’re looking to actually understand how and why these methods work, it’s a great place to start. This is pretty much the standard for graduate classes in adaptive filtering. The techniques in the book can be (and have been) applied to just about every field, from biomedical signals, acoustic signals, to radar signals. This is the text I recommend to just about everyone who is looking to get into any sort of adaptive filtering. A bit of warning though, this book requires a pretty solid background in linear algebra and probability theory to fully appreciate (this is true for most signal processing texts, but this one is especially heavy on notation and mathematics)

If you’re interested in wavelets, “Wavelets: A Concise Guide” by A.H Najmi is a great text. I had Dr. Najmi as a professor for a graduate class and really enjoyed his teaching style. This one is also heavy on math, but again it’s great for understanding the how/why.