Efficient denoising algorithms for large experimental datasets and their applications in Fourier transform ion cyclotron resonance mass spectrometry

TLDR

Measurements are corrupted by random fluctuations, and existing efficient denoising algorithms rely on large matrix analyses that become intractable for moderately large datasets. The authors model a series as an operator applied to random vectors, reducing dimensionality and using simple algebra to robustly denoise data, a method named urQRd that scales to virtually unlimited size. The urQRd method exploits matrix structure for fast, memory‑efficient denoising, uses randomness to reduce noise, and scales to virtually unlimited data sizes.

Abstract

Significance Every measurement is corrupted due to random fluctuations in the sample and the apparatus. Current efficient denoising algorithms require large matrix analysis, and become untractable even for moderately large datasets. Any series can be considered as an operator that modifies any input vector. By applying this operator on a series of random vectors and thus reducing the dimension of the data, it is possible, using simple algebra, to reduce noise in a robust manner. Furthermore, the structure of the underlying matrices allows a very fast and memory-efficient implementation. Counterintuitively, randomness is used here to reduce noise. This procedure, called urQRd (uncoiled random QR denoising), allows denoising to be applied to data of virtually unlimited size.