Multi-resolution signal decomposition level selection

• US 20070053595A1
• Filed: 09/08/2005
• Published: 03/08/2007
• Est. Priority Date: 09/08/2005
• Status: Abandoned Application

• Current Assignee: Honeywell International Inc.
• Original Assignee: Honeywell International Inc.
• Inventors: Eswara, Lalitha
• Application Number:
  US11/222,176
• Publication Number:
  US 20070053595A1
• Time in Patent Office: Days
• US Class Current: 382/233
• CPC Class Codes: G06F 18/00 Pattern recognition
• CPC Class Codes: G06F 2218/08 Feature extraction

Abstract

Multi-resolution Signal Decomposition (MSD) levels for wavelet decomposition are determined automatically in real time. At each level of decomposition, local high frequency variations are eliminated or processed, while gradual patterns present in process control data are considered for further levels of decomposition. These wavelet coefficients are the approximate coefficients, are used for determining the suitable level of MSD. This invention utilizes signal-characterizing properties of these approximate coefficients for identifying suitable MSD levels. In one embodiment, an entropy measure is used and in the other embodiment, fractal dimension is used.

Claims

1. A method of determining a suitable decomposition level of a wavelet transform, the method comprising:

performing a first level of wavelet multi-resolution signal decomposition on an input signal;

determining signal irregularity as a function of signal characterizing properties

determining if a stopping condition has been met as a function of the signal characterizing properties; and

repeating decomposition to more levels until the stopping condition has been met.

2. The method of claim 1 wherein the signal irregularity is a function of a fractal dimension of signal decomposition coefficients.

3. The method of claim 1 wherein the signal irregularity is a function of fractal dimension of an approximated signal at each level.

4. The method of claim 3 and further comprising using a box-counting method to calculate the fractal dimension.

5. The method of claim 4 wherein a slope of a best fit line is used for determining the fractal dimension.

6. The method of claim 2 wherein the stopping condition corresponds to a fractal dimension of less than or equal to one in case of 1-Dimensional signals.

7. The method of claim 2 wherein the stopping condition corresponds to a fractal dimension of less than or equal to one in case of 2-Dimensional signals, leading to the condition that in case of N dimensional signal, the stopping condition corresponds to a fractal dimension of less than or equal to N.

8. The method of claim 1 wherein the signal irregularity is a function of entropy of the input signal.

9. The method of claim 8 wherein the signal irregularity is a further function of approximate coefficients after a first level of decomposition.

10. The method of claim 1 and further comprising further analysis of wavelet coefficients after the stopping condition has been met.

11. The method of claim 1 wherein the input signal corresponds to sensor signals in a process control system.

12. A computer readable medium having instructions stored thereon for causing a computer to perform a method of determining a decomposition level for a wavelet transform, the method comprising:

performing a level of wavelet multi-resolution signal decomposition on an input signal;

determining signal irregularity;

determining if a stopping condition has been met as a function of the signal irregularity; and

repeating decomposition at more levels until the stopping condition has been met.

13. The computer readable medium of claim 12 wherein the signal irregularity is a function of a fractal dimension of signal decomposition coefficients.

14. The computer readable medium of claim 12 wherein the signal irregularity is a function of fractal dimension of an approximated signal at each level.

15. The computer readable medium of claim 12 wherein the stopping condition corresponds to a fractal dimension of less than or equal to one in case of 1-Dimensional signals.

16. The computer readable medium of claim 12 wherein the stopping condition corresponds to a fractal dimension of less than or equal to one in case of 2-Dimensional signals, leading to the condition that in case of N dimensional signal, the stopping condition corresponds to a fractal dimension of less than or equal to N.

17. The computer readable medium of claim 12 wherein the signal irregularity is a function of entropy of the input signal.

18. The computer readable medium of claim 17 wherein the signal irregularity is a further function of approximate coefficients after a first level of decomposition.

19. The computer readable medium of claim 12 and further comprising entropy coding of wavelet coefficients after the stopping condition has been met.

20. The computer readable medium of claim 12 wherein the input signal corresponds to sensor signals in a process control system.

21. A process control system comprising:

means for performing a level of wavelet multi-resolution signal decomposition on an input signal;

means for determining signal irregularity;

means for determining if a stopping condition has been met as a function of the signal irregularity; and

means for repeating decomposition at more levels until the stopping condition has been met.

22. A method of wavelet transform comprising:

performing a first level wavelet decomposition by filtering an input signal through a HPF and LPF wavelet filter bank to capture first level output coefficients;

determining irregularity characteristics of the LPF output coefficient based on signal characterizing properties pertaining to said LPF output coefficient; and

determining the necessity of further wavelet decomposition after the first level decomposition based on said irregularity measures.

23. The method of claim 22 wherein said properties are selected from the group consisting of fractal dimension and entropy of said LPF output coefficients.