CW ESR denoising – when triplets meet wavelets Boris Dzikovski, ACERT
Denoising with wavelets - Popular in signal processing since 1990s - Wavelet transform leads to a sparse representation for many real-world signals. - Wavelet coefficients which are small in value are considered noise and can be removed without affecting the signal. - Wavelet denoising results in better approximations of the original signal compared to e.g. Fourier filtering etc. - The new method with intelligent thresholding allows for recovering signals even for seemingly hopeless cases.
Nicer and smoother, yes. But is it more informative? Tempo in water Can we extract more information by denoising? 0.02 And the answer is: N O Magnitude Yes! 0 Extracting polarity/mobility parameters from -0.02 Noisy a iso = 17.18G, τ = 1.2×10 -11 s a iso = 17.25G, τ = 1.7×10 -11 s Denoised 3340 3350 3360 3370 3380 3390 “No noise” spectrum a iso = 17.25G, τ = 1.8×10 -11 s Magnetic Field, G noisy long accamulation denoised Tempo in water/glyc, 100K Extracting D 1 /D parameter from Noisy 0.507 D 1 D Denoised 0.414 “No noise” spectrum 0.413 3280 3300 3320 3340 3360 3380 Magnetic Field, G
Extracting super hyperfine structures Tempol in CCl 4 , deoxygenated noisy denoised OH long accumulation N O noisy denoised 3322 3323 3324 3325 Magnetic Field, G 3290 3300 3310 3320 3330 3340 3350 3360 Magnetic Field, G
Miracles are not guaranteed O 0.2 0.2 N SNR ≤ 0.25 0.1 SNR ~ 1 0.1 O Magnitude Magnitude 0 0 -0.1 -0.1 -0.2 -0.2 3140 3160 3180 3200 3220 3140 3160 3180 3200 3220 Magnetic Field, G Magnetic Field, G Tempone in water – the ability to extract single very fine features meets its limits.
But miracles happen – sometimes. di- p - tert -butyl-phenyl nitroxide in toluene, degassed noisy denoised N long accumulation O And such spectra are not uncommon: N Pyrazine anion - N . 2Cl- + CH3 H3C N + N Methyl Viologen ] - [ H2C C C CH2 3300 3320 3340 Butadien ion Magnetic Field, G
Denoising is able to reveal underresolved hyperfine splitting features: Same experimetal sample, Two different amplitude modulation: M=0.2G M=1G Detail components 2-3-4 kept but approximation component put to zero
Spin trapping, a lot of weak signals. Much better with denoising. noisy denoised reference signal + •OH • In some spin-trapping experiments without denoising the very presence of a trapping adduct is uncertain. Denoising allows for reliable identification and quantification of the reaction products. 3300 3320 3340 Magnetic Field, G
ENDOR – another case of traditionally weak signals Both pulse (Mims and in particular Davies) and CW ENDOR require very long accumulation time due to low sensitivity. A lot of opportunities to apply denoising techniques at various stages of spectral processing: From denoising single transients to the CW-style denoising of the resulting ENDOR spectrum 6 4 10 10 0 Original Signal Denoised Signal 3 PD-Tempone in D 2 O/d 8 -glyc -2 with some H 2 O content, 2.5 -4 Davies ENDOR 2 -6 1.5 -8 1 -10 0.5 -12 0 -14 Biological tyrosyl radical – Mims Endor -0.5 -16 -1 -18 42 44 46 48 50 52 54 56 58 5 10 15 20 25 30 35 40 45 50 55
CW ESR = multiple scans (usually) PC spin label in liposomes of mixed lipids Choosing “good” scans using wavelet denoising – “scan sorting”.
Should we average denoised scans? Every scan denoised Denoised after accumulation 95 GHz 95 GHz Magnetic Field, Tesla Magnetic Field, Tesla Better to denoise after averaging…
Real or Ghost? Testing spectral features by using alternating set of scans with following denoising. Even scans Odd scans Still here
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