Methods for performing DAF data filtering and padding

• US 6,847,737 B1
• Filed: 03/12/1999
• Issued: 01/25/2005
• Est. Priority Date: 03/13/1998
• Status: Expired due to Term

• Current Assignee: Iowa State University, University of Houston System
• Original Assignee: Iowa State University Research Foundation Incorporated (Iowa State University), University of Houston System
• Inventors: Shi, Zhuoer, Wei, G. W., Bao, Zheng, Hoffman, David K., Kouri, Donald J., Kakadiaris, Ioannis, Zhang, DeSheng, Wang, Haixiang, Gunaratne, Gemunu H.
• Primary Examiner(s): Rogers, Scott
• Application Number:
  US09/266,963
• Time in Patent Office: 2,146 Days
• Field of Search: 382/260, 382/264, 382/275, 382/300, 708/300, 708/313
• US Class Current: 382/260
• CPC Class Codes: G06F 2218/06 by applying a scale-space analysis, e.g. using wavelet analysis
• CPC Class Codes: G06T 2207/20064 Wavelet transform [DWT]
• CPC Class Codes: G06T 2207/20084 Artificial neural networks [ANN]
• CPC Class Codes: G06T 2207/20192 Edge enhancement; Edge preservation
• CPC Class Codes: G06T 5/10 using non-spatial domain filtering
• CPC Class Codes: G06T 5/20 using local operators
• CPC Class Codes: G06T 5/60 using machine learning, e.g. neural networks
• CPC Class Codes: G06T 5/70 Denoising; Smoothing
• CPC Class Codes: G06V 10/30 Noise filtering

Abstract

A method for padding, filtering, denoising, image enhancing and increased time-frequency acquisition is described for digitized data of a data set where unknown data is estimated using real data by adding unknown data points in a manner that the padding routine can estimate the interior data set including known and unknown data to a given accuracy on the known data points. The method also provides filtering using non-interpolating, well-tempered distributed approximating functional (NIDAF)-low-band-pass filters. The method also provides for symmetric and/or anti-symmetric extension of the data set so that the data set may be better refined and can be filtered by Fourier and other type of low frequency or harmonic filters.

Claims

1. A method for data padding and noise filtering implemented on a digital processing device, comprising the steps of:

a. defining a total data set as the collection of all known and unknown data, where the unknown values may be interspersed among the known values, or concentrated in a region adjacent to the known values, or a combination of the two;

b. placing the unknown values of the data to be obtained by a padding procedure so that the total data set contains only equally space data—

the data has a constant sampling interval and the total data set represents a function;

c. calculating an appropriate difference between the true data and an approximation to the data for all known and unknown data values;

d. minimizing the difference with respect to the unknown data values by iteration or using the calculus of variations to obtain algebraic equations for the unknown values or solving the algebraic equation for the unknown data values.

2. The method of claim 1, further comprising the step of:

e. removing a noise from the total data set using a non-interpolating, well-tempered distributed approximating functional (NIDAF)-low-band-pass filter to form an approximation to the total data set.

3. The method of claim 1, wherein the data is a time-sequence of multi-dimensional data.

4. The method of claim 2, wherein time-sequence is a 2-dimensional sampling of an image at a fixed time interval.

5. The method of claim 1, wherein the data is 1-dimensional data.

9. The method of claim 2, further comprising:

b. when the known input data set comprises a finite number of evenly spaced (or sampled), but sequential data points, adding interspersed unknown data points to construct an evenly spaced or sampled data set to form an augments evenly spaced sequential data set, adding a gap with unknown data having the same spacing or sampling rate and then repeating the augmented evenly spaced sequential data set after the gap to form a periodic, evenly spaced extension of the known data where the extension have the same or opposite sign of the augmented data set where a same sign extension yields a symmetric periodic extended data set and an opposite sign yields an anti-symmetric periodic extended data set;

c. calculating an appropriate difference between the true data (known and unknown, including gap and interspersed unknown data) and a DAF approximation to the total data set and choosing DAF parameters so the largest estimated or predicted data do not exceed the largest known input data, and so that the lowest estimated or predicted data are not less than the lowest known input data;

d. minimizing this difference with respect to the unknown data values and gap and interspersed unknown data by iteration or using the calculus of variations to obtain algebraic equations for the unknown values or solving the algebraic equations for the unknowns.

10. A method for image processing implemented on a digital processing device, comprising the steps of:

associating data of an image with a group of points;

associating a measure of disorder parameter with the data of the image;

padding the data and periodically extending it as in claim 4 or 5, using a DAF approximation to the data with the DAF parameters chosen so that the largest estimated or predicted data values do not exceed the largest known input data and the lowest estimated or predicted data values are not less than the lowest know input data;

filtering out the noise by using a well-tempered NIDAF-low-band-pass-filter to approximate the total data set and calculating the disorder parameter as a function of the DAF parameters M and σ

|Δ

. The change in the disorder parameter as a function of σ

|Δ

(for a given M) will be used as the indicator for the optimum well-tempered NIDAF-low-band-pass-filter;

if desired, one can also use the periodically extended and filtered total data set to carry out further standard Fourier filtering.

11. The method of claim 10, further comprising:

categorizing the images and patterns using the final disorder parameter;

images or patterns with the same disorder parameter will be assumed to be similar;

a catalogue of such images or patterns, and their corresponding disorder parameters, will be used to construct a comparison and categorization of surface roughness, as well as other properties that generate images and patterns;

similar catalogues of such images and/or patterns of stressed materials will be used to identify incipient structural flaws or weakness;

similar catalogues of fractured or on-going fracturing materials will be used to identify microscopic fractures or structural flaws;

similar catalogues of patterns associated with any kind of defect will be constructed and used for predictive diagnostics.

6. A method for data padding and noise filtering implemented on a digital processing device, comprising the steps of:

a. defining a total data set as the collection of all known and unknown data, where the unknown values may be interspersed among the known values, or concentrated in a region adjacent to the known values, or a combination of the two;

b. placing the unknown values of the data to be obtained by a padding procedure so that the total data set contains only equally space data—

the data has a constant sampling interval and the total data set represents a function;

c. calculating an appropriate difference between the true data of the total data set and a DAF approximation to the data for all known and unknown data values; and

d. minimizing the difference with respect to the unknown data values by iteration or by using the calculus of variations to obtain algebraic equations for the unknown values or solving the algebraic equation for the unknown data values.

7. The method of claim 6, further comprising:

b. when the known input data set comprises a finite number of sequential data values having an evenly spaced distribution, adding a gap of a finite number of unknown data having the same spacing or sampling rate and some other functional dependence or tail function;

c. calculating an appropriate difference between the true data (known and unknown, including gap points and tail function points) and a DAF approximation to the data values including values at gap points and the unknown coefficients in the tail function or sum of basis functions and choosing DAF parameters so that the largest predicted or estimated data values do not exceed the largest known input values and the lowest estimated or predicted data values are not less than the lowest known input values; and

d. minimizing this difference with respect to all unknown values and coefficients by iteration or by using the calculus of variations to obtain algebraic equations for the unknowns or solving the algebraic equations for the unknowns.

8. The method of claim 6, further comprising:

b. when the known data set comprises a finite number of evenly spaced, sequential data points, adding a gap with a finite number of data point having the same spacing or sampling rate and adding a repetition of the finite number of evenly spaced, sequential data points to give a periodic extension of the known input data, where a sign associated with the periodic extension is the same or opposite of the input dat and where the same sign periodic extension yields a symmetric extension of known input data and the opposite sign periodic extension yields an anti-symmetric extension of known input data;

c. calculating an appropriate difference between the true data (known and unknown, including gap points) and a DAF approximation to this data and choosing DAF parameters so the largest estimated or predicted data do not exceed the largest known input data and the lowest estimated or predicted data are not less than the lowest known input data; and

d. minimizing this difference with respect to the unknown data values by iteration or using the calculus of variations to obtain algebraic equations for the unknown values or solving the algebraic equations for the unknown gap data values.

12. A method for data padding and noise filtering implemented on a digital processing device, comprising the steps of:

a. defining a total data set as the collection of all known and unknown data, where the unknown values may be interspersed among the known values, or concentrated in a region adjacent to the known values, or a combination of the two;

b. placing the unknown values of the data to be obtained by a padding procedure so that the total data set contains only equally space data—

the data has a constant sampling interval and the total data set represents a function;

c. calculating an appropriate difference between the true data of the total data set and a DAF approximation to the data for all known and unknown data values;

d. solving the algebraic equation for the unknown data values.

13. The method of claim 12, further comprising the step of:

e. removing a noise from the total data set using a non-interpolating, well-tempered distributed approximating functional (NIDAF)-low-band-pass filter to form an approximation to the total data set.