When I was in #CS grad school, back in the early 1990s, #wavelets were hot in 3D volumetric CG—oh, those SIGGRAPH symposia on the topic. At the same time in #EE, loads of papers were published on their efficacy in DSP. Just about everyone in EE and CS seemed to have published at least one paper on wavelets. Fun times. But the current state of wavelet academic #research seemed to have dried up.

I don't quite understand why wavelet transform has not supplanted Fourier transform in many #engineering and #computing application domains, considering its estimable time-frequency locality and its prodigious multi-resolution analysis capabilities, compared to Fourier analysis.

I am but a mere "maths carpenter". So, what am I missing, I wonder.

Wavelet-Based Spectrum Analyzer! 🎶

FFT has long been the go-to method for visualizing audio spectra, but what if there’s a faster and more efficient alternative? Enter the Haar Wavelet Transform: a technique that provides logarithmic frequency resolution while being even more computationally efficient than FFT-based analysis.

Stay tuned for a deep dive into how wavelets can be used for real-time spectral analysis—no FFTs required!

Some preview: https://gist.github.com/ashafq/99d468dc5e52c7bea23ad4824e21161f

#dsp #wavelets #audio #programming #signalprocessing

MotionWavelet: Human Motion Prediction via Wavelet Manifold Learning

Authors: Yuming Feng, Zhiyang Dou, Ling-Hao Chen, Yuan Liu, Tianyu Li, Jingbo Wang, Zeyu Cao, Wenping Wang, Taku Komura, Lingjie Liu

pre-print -> https://arxiv.org/abs/2411.16964
website -> https://frank-zy-dou.github.io/projects/MotionWavelet/

#motion_prediction #wavelets #diffusion

'ptwt - The PyTorch Wavelet Toolbox', by Moritz Wolter, Felix Blanke, Jochen Garcke, Charles Tapley Hoyt.

http://jmlr.org/papers/v25/23-0636.html

#wavelet #wavelets #pytorch

☕ Here's a bit of technical content from me - today a deep dive on #baseline correction methods.

📈 Baseline correction is a preprocessing technique to remove background signal and isolate peaks in hashtag#spectroscopy data.

📝 In my recent post I discuss two methods:
1. Wavelet transform (WT) - Decomposes signal into components at different frequencies. Lowest frequency component represents baseline and can be removed.
2. Asymmetric least squares (ALS) - Fits a smooth baseline function, penalising positive deviations more than negative ones.

TL;DR: WT method is intuitive but can distort peaks. ALS produces better results.

🔎 Both methods are applied on a #Raman spectrum and an X-ray fluorescence (#XRF) spectrum. ALS gives a cleaner baseline correction and it's effective for removing broad, slowly varying background while preserving sharper spectral features.

#chemometrics #Python #MachineLearning #wavelets #regression

https://nirpyresearch.com/two-methods-baseline-correction-spectral-data/

𝗝𝗼𝘂𝗿𝗻𝗮𝗹 𝗼𝗳 𝗘𝗻𝘃𝗶𝗿𝗼𝗻𝗺𝗲𝗻𝘁𝗮𝗹 & 𝗘𝗮𝗿𝘁𝗵 𝗦𝗰𝗶𝗲𝗻𝗰𝗲𝘀 | 𝗩𝗼𝗹𝘂𝗺𝗲 𝟬𝟰 | 𝗜𝘀𝘀𝘂𝗲 𝟬𝟮 | 𝗢𝗰𝘁𝗼𝗯𝗲𝗿 𝟮𝟬𝟮𝟮

𝗝𝗼𝘂𝗿𝗻𝗮𝗹 𝗼𝗳 𝗘𝗻𝘃𝗶𝗿𝗼𝗻𝗺𝗲𝗻𝘁𝗮𝗹 & 𝗘𝗮𝗿𝘁𝗵 𝗦𝗰𝗶𝗲𝗻𝗰𝗲𝘀 | 𝗩𝗼𝗹𝘂𝗺𝗲 𝟬𝟰 | 𝗜𝘀𝘀𝘂𝗲 𝟬𝟮 | 𝗢𝗰𝘁𝗼𝗯𝗲𝗿 𝟮𝟬𝟮𝟮 🌏 Quantum Biophysics of the Atmosphere: Asymmetric Wavelets of the Average Annual Air Temperature of Irkutsk for 1820-2019 👉 The regularities of the dynamics of the average annual temperature of Irkutsk from 1820 to 2019 were revealed. #Averageannualtemperature #1820to2019 #Wavelets #Forecastupto2220 🔗 DOI: ✉…

https://myfavorite621.wordpress.com/2023/12/11/%f0%9d%97%9d%f0%9d%97%bc%f0%9d%98%82%f0%9d%97%bf%f0%9d%97%bb%f0%9d%97%ae%f0%9d%97%b9-%f0%9d%97%bc%f0%9d%97%b3-%f0%9d%97%98%f0%9d%97%bb%f0%9d%98%83%f0%9d%97%b6%f0%9d%97%bf%f0%9d%97%bc%f0%9d%97%bb/

"Binlets: Data fusion-aware denoising enables accurate and unbiased quantification of multichannel signals", Silberberg & Grecco, 2023 https://www.sciencedirect.com/science/article/pii/S1566253523003159

Old school signal processing, not based on machine learning but instead on a translation-invariant Haar wavelet decomposition, profitably exploiting correlations across channels. The manuscript includes an accessible and brief "Theory" section and a longer appendix. All it needs to run is a test function between two data points.

In their benchmarks and use cases, the new method outperforms existing denoising methods. In both time series and on fluorescent microscopy images.

There's a repository available https://github.com/maurosilber/binlets and can be installed with `pip install binlets`.

#denoising #SignalProcessing #wavelets #ComputerVision

Wavelet decomposition is very popular in image analysis and processing. Here's my attempt to share some code to perform spectral smoothing (or denoising, to be fancy) using the same principle.

Wavelet denoising of spectra • NIRPY Research
https://nirpyresearch.com/wavelet-denoising-spectra/

#ImageProcessing #chemometrics #spectroscopy #wavelets #DataProcessing