Extraction of Weak Spectroscopic Signals with High Fidelity: Examples from ESR

Noise impedes experimental studies by reducing signal resolution and/or suppressing weak signals. Signal averaging and filtering are the primary methods used to reduce noise, but they have limited effectiveness and lack capabilities to recover signals at low signal-to-noise ratios (SNRs). We utilize a wavelet transform-based approach to effectively remove noise from spectroscopic data. The wavelet denoising method we use is a significant improvement on standard wavelet denoising approaches. We demonstrate its power in extracting signals from noisy spectra on a variety of signal types ranging from hyperfine lines to overlapped peaks to weak peaks overlaid on strong ones, drawn from electron-spin-resonance spectroscopy. The results show that one can accurately extract details of complex spectra, including retrieval of very weak ones. It accurately recovers signals at an SNR of ∼1 and improves the SNR by about 3 orders of magnitude with high fidelity. Our examples show that one is now able to address weaker SNR signals much better than by previous methods. This new wavelet approach can be successfully applied to other spectroscopic signals.