Systems, methods and programs for denoising signals using wavelets

Patent metadata

Field	Value
Publication number	US-10891719-B2
Application number	US-201716301209-A
Country	US
Kind code	B2
Filing date	May 11, 2017
Priority date	May 11, 2016
Publication date	Jan 12, 2021
Grant date	Jan 12, 2021

Abstract

Methods, systems and programs for denoising a signal using discrete wavelet transformation are provided. For example, a method for denoising a signal may include determining a number of resolution levels to denoise, determining variable threshold(s) for each resolution level, applying the determined variable threshold(s) to denoise at least a detail component of each of the determined resolution levels. Each variable threshold includes a separately determined lower threshold and upper threshold. The method for denoising a signal may further include transforming, using an inverse discrete wavelet transformation, at least the denoised detail component for each of the determined resolution levels into a denoised signal.

First claim

What is claimed is:

1. A method of denoising a signal comprising:
transforming a signal using a discrete wavelet transformation into a first wavelet component and a second wavelet component for each of a plurality of different resolutions, respectively, using preset wavelets, each of the first wavelet component and the second wavelet component having a plurality of coefficients;
determining a number of different resolutions, where the number is k, of the plurality of different resolutions for use in thresholding by examining at least coefficients for the first wavelet component for at least two of the plurality of different resolutions, respectively;
for each of the determined number of different resolutions for use in thresholding, comparing each coefficient in the first wavelet component with a variable threshold, the variable threshold for each of the determined number of different resolutions being different, and selectively changing a value of the coefficient based on the comparison thereby generating a modified first wavelet component having changed coefficients and unchanged coefficients;
for the kth different resolution, comparing each coefficient in the second wavelet component with a second variable threshold, and selectively changing a value of the coefficient based on the comparison, thereby generating a modified second wavelet component having changed coefficients and unchanged coefficients; and
transforming, using an inverse discrete wavelet transformation, the modified first wavelet component for each of the determined number of resolutions and the modified second wavelet component into a denoised signal.

2. The method of denoising a signal according to claim 1 , wherein k is based on a comparison of a maximum value to sum value ratio of values of the coefficients for the first wavelet component with a decomposition threshold for at least two of the plurality of different resolutions.

3. The method of denoising a signal according to claim 2 , wherein the determining of k comprises:
calculating the maximum value to sum value ratio for two different resolutions;
comparing the maximum value to sum value ratio for the two different resolutions with the decomposition level threshold, wherein if the maximum value to sum value ratio of one of the two different resolutions is greater than the decomposition level threshold, k is determined at 2, wherein if the maximum value to sum value ratio for both different resolutions is less than or equal to the decomposition level threshold, the determining of k further comprises:
calculating the maximum value to sum value ratio for an additional different resolution and comparing the calculated the maximum value to sum value ratio for the additional different resolution with the decomposition level threshold, repeatedly, until the maximum value to sum value ratio for an additional different resolution is greater than the decomposition level threshold, and
wherein when the calculated maximum value to sum value ratio for an additional different resolution is greater the decomposition level threshold, k is determined as a total number of times the maximum value to sum value ratio was calculated minus 1.

4. The method of denoising a signal according to claim 1 , further comprising displaying the first wavelet component and the second wavelet component, respectively, for each of a plurality of different resolutions and wherein k is based on a visual inspection of at least the first wavelet component for a subset of the plurality of different resolutions.

5. The method of denoising a signal according to claim 1 , the variable threshold comprises a lower variable threshold and an upper variable threshold.

6. The method of denoising a signal according to claim 5 , 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.

7. The method of denoising a signal according to claim 5 , wherein coefficients having values between the lower variable threshold and the upper variable threshold are reduced as the change.

8. The method of denoising a signal according to claim 7 , wherein the reduction is to zero.

9. The method of denoising a signal according to claim 5 , further comprising:
determining the lower variable threshold for each of the determined number of different resolutions; and
determining the upper variable threshold for each of the determined number of different resolutions, wherein the lower variable threshold and the upper variable threshold is separately determined.

10. The method of denoising a signal according to claim 9 , wherein for each of the determined number of different resolutions for use in thresholding, the lower variable threshold is determined using an average value of the coefficients for the first wavelet component for that resolution, a standard deviation of the coefficients for the first wavelet component for that resolution and a first scaling factor for the standard deviation for that resolution, and the lower variable threshold is determined using an average value of the coefficients for the first wavelet component for that resolution, a standard deviation of the coefficients for the first wavelet component for that resolution and a second scaling factor for the standard deviation for that resolution.

11. The method of denoising a signal according to claim 10 , further comprising:
displaying the first wavelet component and the second set of wavelet component, respectively, for each of a plurality of different resolutions and the modified first wavelet component for each of the determined number of different resolutions and the modified second wavelet component;
comparing, visually the first wavelet component and the modified first wavelet component for each of the determined number of different resolutions; and
adjusting the first scaling factor and the second scaling factor for at least one resolution based on the comparing.

12. A method of denoising a signal comprising:
reversing in time, a signal;
transforming the time reversed signal using a discrete wavelet transformation into a first wavelet component for each of a number of different resolutions, wherein the number of different resolutions is k and a second wavelet component for the kth different resolution, each of the first wavelet component and the second wavelet component for the kth different resolution having a plurality of coefficients;
for each of the number of different resolutions,
dividing coefficients for the first wavelet components into a first-subset of coefficients and a second-subset of coefficients based on a determined signal to noise ratio;
comparing each coefficient in the first-subset of coefficient with a first variable threshold, the first variable threshold for each of the number of different resolutions being different, and selectively changing a value of the coefficient in the first-subset of coefficients based on the comparison thereby generating a modified first subset of coefficients having changed coefficients and unchanged coefficients;
comparing each coefficient in the second-subset of coefficients with a second variable threshold, the second variable threshold for each of the number of different resolutions being different, and selectively changing a value of the coefficient in the second-subset of coefficients based on the comparison thereby generating a modified second subset of coefficients having changed coefficients and unchanged coefficients; and
combining the modified first subset of coefficients with the second subset of coefficients,
transforming, using an inverse discrete wavel

Assignees

• Univ Cornell

Inventors

• Srivastava Madhur
• Freed Jack H
• Anderson C Lindsay

Classifications

• G06T2207/20016

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

• G06T5/10

  using non-spatial domain filtering · CPC title

• G06T2207/20064

  Wavelet transform [DWT] · CPC title

• G06F17/148

  Wavelet transforms · CPC title

• A61B5/726

  using Wavelet transforms · CPC title