Wavelet denoising using signal location windowing

Patent metadata

Field	Value
Publication number	US-12423780-B2
Application number	US-202118012426-A
Country	US
Kind code	B2
Filing date	Jun 24, 2021
Priority date	Jun 24, 2020
Publication date	Sep 23, 2025
Grant date	Sep 23, 2025

Abstract

Methods, systems and programs for denoising a signal using an undecimated discrete wavelet transformation are provided. The methods use signal location windows. The signal location windows may be used before or after thresholding. When signal location windows are used after thresholding coefficients within the signal location windows may be restored to their original values. When signal location windows are used before thresholding, coefficients within the signal location windows may be unchanged by the thresholding. The signal location windows may be used only on a subset of decomposition levels that are thresholded. The signal location windows may be used on both the Detail components and the highest decomposition level for thresholding of the Approximation component.

First claim

What is claimed is:

1. A method of denoising a signal comprising:
transforming a signal using an undecimated discrete wavelet transformation into at least a first wavelet component, the first wavelet component having a plurality of coefficients, the first wavelet component having a plurality of decomposition level, where a number of the plurality of coefficients in each level are the same;
for each decomposition level determined for thresholding, comparing each coefficient of the plurality of coefficients with a threshold, and selectively changing a value of the coefficient based on the comparison thereby generating a first modified first wavelet component having changed coefficients and unchanged coefficients for a decomposition level;
positioning one or more windows on the first modified first wavelet component for a highest decomposition level determined for thresholding, by evaluating the changed coefficients and unchanged coefficients in the first modified first wavelet component for the highest decomposition level;
changing coefficients in the first modified first wavelet component for the highest decomposition level determined for thresholding to its original value when the coefficients are within the one or more windows while keeping the coefficients outside the one or more windows the same as in the first modified first wavelet component to generate a second modified first wavelet component for the highest decomposition level determined for thresholding;
positioning the one or more windows on the first modified first wavelet component for a subset of other decomposition levels of the plurality of decomposition levels at the same positions;
changing coefficients in the first modified first wavelet component for each of the subset of other decomposition levels to its original value when the coefficients are within the one or more windows while keeping the coefficients outside the one or more windows the same as the first modified first wavelet component to generate a third modified first wavelet component, respectively, for each decomposition level of the subset of other decomposition levels; and
transforming, using an inverse undecimated discrete wavelet transformation, the first modified first wavelet component for decomposition levels other than the subset of other decomposition levels and the highest decomposition level, respectively, the second modified first wavelet component for the highest decomposition level and the third modified first wavelet component for the subset of other decomposition levels, respectively, into a denoised signal.

2. The method of denoising a signal according to claim 1 , wherein the subset of other decomposition levels does not include decomposition levels having coefficients only containing noise.

3. The method of denoising a signal according to claim 1 , wherein the position of each of the one or more windows is such that the ends of the one or more windows are where a value of the coefficients change from non-zero to zero and zero to non-zero.

4. The method of denoising a signal according to claim 1 , further comprising determining a number of the plurality of decomposition levels for thresholding by examining at least coefficients for the first wavelet component for at least two different decomposition levels.

5. The method of denoising a signal according to claim 1 , wherein the threshold for each decomposition level determined for thresholding is variable.

6. The method of denoising a signal according to claim 5 , wherein the threshold for each decomposition level determined for thresholding is different.

7. The method of denoising a signal according to claim 6 , wherein the threshold for each decomposition level determined for thresholding comprises a lower threshold and an upper threshold and the lower variable threshold is a negative value and compared to negative coefficients and the upper variable threshold is a positive value and compared to positive coefficients.

8. The method of denoising a signal according to claim 7 , wherein coefficients having values between the lower variable threshold and the upper variable threshold are reduced as the change.

9. The method of denoising a signal according to claim 1 , further comprising:
transforming a signal using an undecimated discrete wavelet transformation into the first wavelet component and a second wavelet component, both the first wavelet component and the second wavelet component having a plurality of coefficients, the first wavelet component and the second wavelet component having a plurality of decomposition levels, where the number of the plurality of coefficients in each level are the same;
for the highest decomposition level determined for thresholding, comparing each coefficient in the second wavelet component with a second threshold, and selectively changing a value of the coefficient based on the comparison, thereby generating a first modified second wavelet component having changed coefficients and unchanged coefficients;
positioning one or more windows on the first modified second wavelet component for a highest decomposition level determined for thresholding, by evaluating the changed coefficients and unchanged coefficients in the first modified second wavelet component for the highest decomposition level determined for thresholding;
changing coefficients in the first modified second wavelet component for the highest decomposition level determined for thresholding to its original value when the coefficients are within the one or more windows while keeping the coefficients outside the one or more windows the same as the first modified second wavelet component to generate a second modified second wavelet component; and
transforming, using an inverse undecimated discrete wavelet transformation, the first modified first wavelet component for decomposition levels other than the subset of other decomposition levels and the highest decomposition level, respectively, the second modified first wavelet component for the highest decomposition level, the third modified first wavelet component for the subset of other decomposition levels, respectively, and the second modified second wavelet component, into the denoised signal.

10. The method of denoising a signal according to claim 9 , wherein the position of the one or more windows on the second wavelet component is different than the position of the one or windows on the first wavelet component.

11. The method of denoising a signal according to claim 2 , further comprising determining whether a decomposition level contains all noise.

12. The method of denoising a signal according to claim 11 , wherein the determining is based on whether a maximum coefficient value for the decomposition level divided by a sum of all coefficient values for the decomposition level is less than a sparsity threshold.

13. The method of denoising a signal according to claim 1 , wherein the signal is a scan or an average of scans from an electron spin resonance (ESR)-based pulsed dipolar spectroscopy.

14. The method of denoising a signal according to claim 1 , wherein the signal has a signal to noise ratio for a peak greater than 0.5.

15. The method of denoising a signal according to claim 1 , wherein a signal to noise ratio for a peak is increased by at least three orders of magnitude in the denoised signal than in the signal.

16. The method of denoising a signal according to claim 1 , further comprising:
displaying the first modified first wavelet component having changed coefficients and unchanged coefficients for each decomposition level; and
determining the positio

Assignees

• Univ Cornell

Inventors

• Srivastava Madhur
• Freed Jack H

Classifications

• G06T2207/20064

  Wavelet transform [DWT] · CPC title

• G06T2207/20016

  Hierarchical, coarse-to-fine, multiscale or multiresolution image processing; Pyramid transform · CPC title

• G06F17/148 Primary

  Wavelet transforms · CPC title

• A61B5/7203

  for noise prevention, reduction or removal · CPC title

• G06T5/70 Primary

  Denoising; Smoothing · CPC title