Haar Transform Denoising for Poisson Noise in Diffraction Data
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Solution Overview
Problem
Existing methods for denoising diffraction data, such as those using Fourier analysis or wavelets, are not well-suited for handling Poisson noise, which is inherent in count data, leading to inaccurate results and preservation of noise in the data.
Innovation Solution
The method employs a Haar transform to denoise diffraction data sets with Poisson noise, utilizing a hard thresholding rule specifically designed for the Poisson noise distribution, along with cycle spinning to improve results, thereby effectively removing noise while preserving signal features.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-affected harmful factors
If digital filters such as moving average or Savitsky-Golay filtering are used to smooth diffraction data, then noise is reduced, but sharp peaks are broadened and maximum intensity is reduced
Solution Approach 1:
The patent changes the fundamental parameter of the filtering approach by using wavelet transform instead of traditional digital filters. Wavelets provide adaptive smoothing that preserves peak sharpness by transforming the data into a different domain where noise and signal can be separated more effectively, then transforming back while maintaining original peak characteristics.
Solution Approach 2:
The patent replaces mechanical smoothing operations (moving average, Savitsky-Golay filters) with a mathematical transformation approach (wavelet transform). This substitution allows for more sophisticated noise removal that doesn't rely on simple averaging, thereby preserving sharp features in the diffraction pattern.
2Object-affected harmful factors
If Fourier analysis with low-pass filters is used to denoise diffraction data, then high frequency noise is removed, but sharp peaks lose their high-frequency components resulting in undershoot and ringing artifacts
Solution Approach 1:
The patent substitutes Fourier transform-based filtering with wavelet transform. Wavelets provide localized frequency analysis that preserves the high-frequency components necessary for sharp peaks while still removing noise, avoiding the artifacts inherent in Fourier-based low-pass filtering.
Solution Approach 2:
The patent applies local quality by using wavelets that can adapt to local features in the data. Different regions of the diffraction pattern can be smoothed with different levels of aggressiveness, preserving sharp peaks while removing noise from broader features, unlike global Fourier filtering that applies the same smoothing across the entire spectrum.
3Measurement precision
If more photons are counted to improve signal-to-noise ratio, then Poisson noise is reduced, but analysis time increases and sample throughput decreases
Solution Approach 1:
The patent applies preliminary action by collecting data with sufficient photons to achieve an acceptable initial signal-to-noise ratio, then using wavelet denoising as a post-processing step to further reduce noise. This allows for shorter initial data collection times while achieving the desired final quality through computational enhancement.
Solution Approach 2:
The patent introduces wavelet transform as an intermediary processing step between raw data collection and final analysis. This intermediary computational process enhances the signal-to-noise ratio without requiring additional physical measurement time, thereby maintaining high sample throughput while improving measurement precision.
4Manufacturing precision
If narrow diffractometer slits and narrow band-pass monochromators are used to improve peak resolution, then peak resolution is enhanced, but signal-to-noise characteristics deteriorate
Solution Approach 1:
The patent uses wavelet transform as an intermediary computational tool that can enhance peak resolution further after data collection with broader slits and monochromators. This computational enhancement allows for improved peak resolution without the penalty of reduced signal-to-noise ratio that would result from using narrower physical apertures.
Data Source
AI summary
A method for generating a denoised data set from a data set comprising a signal and Poisson noise is disclosed. The method includes applying, by a data set denoising computing device, a Haar transform to the data set to generate a Haar transformed data set. The Haar transformed data set is denoised using a thresholding rule based on the Haar transformed data set to remove the Poisson noise from the signal. A reverse Haar transform is applied to the denoised Haar transformed data set to generate the denoised data set. A data set denoising computing device and non-transitory computer readable medium for performing the method are also disclosed.