Spatial frequency feature extraction for a classification system using wavelets

• US 5,757,309 A
• Filed: 12/18/1996
• Issued: 05/26/1998
• Est. Priority Date: 12/18/1996
• Status: Expired due to Fees

• Current Assignee: the united states of america as represented by the secretary of the navy
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: Brooks, Harold Aurelius, Reade, David Leslie, Roth, Duane
• Primary Examiner(s): Sotomayor, John B.
• Application Number:
  US08/769,721
• Time in Patent Office: 524 Days
• Field of Search: 342/64, 342/90, 342/135, 342/192, 342/193, 342/194, 342/195, 342/196, 364/485, 364/728.01, 364/486, 364/484, 364/421, 364/422, 364/724.12, 364/728.03, 364/487, 364/726
• US Class Current: 342/90
• CPC Class Codes: G01S 7/411 Identification of targets based on measurements of radar reflectivity G01S7/415 takes precedence
• CPC Class Codes: G06T 9/007 Transform coding, e.g. discrete cosine transform

Abstract

An iterative process to determine the wavelet function and combination of ales of the function which provides data where there is a large separability compared to the separability of the data set prior to processing. Wavelets are selected for inclusion in a library in accordance with predetermined criteria and then applied to a digitized signal by convolution to perform digital filtering. The convolution of each wavelet is performed for the number of times dictated by the coefficients of the wavelet for each of the input signal samples. Separability of the wavelet implemented digital filtration is calculated as a percentage for each wavelet. The separation data is stored in memory until the iterative process is applied to all wavelets. The separability data is then examined to identify the wavelet producing the greatest separation. The data separability is estimated using a likelihood ratio after the probability densities for each of two sets of profile data are estimated. The lower and upper bounds for a Bayes error are determined using resubstitution (R) and leave one out (L) methods, respectively.

Claims

1. A computerized apparatus for extracting spatial frequency features in two sets of range profiles for two targets for a classification system using wavelets for digital filtering, said computerized apparatus comprising:

a library of wavelets having shapes, coefficients and computational efficiency consistent with the dictates of an application;

means for selecting a wavelet from said library of wavelets;

means for selecting a scale to be used in applying said wavelet;

means for inputing a set of analog range profiles, one set of said analog range profiles being input for each of said two targets;

means for digitizing said analog range profiles for each of said two targets;

an iterative digital processing means for successively and exhaustively applying each selected wavelet at each of its selected scales to digitally filter each of said two sets of digitized range profiles;

said iterative digital processing means computing the separability of the data in each of said two sets of digitized range profiles until a wavelet and scale is identified with a calculation of maximum separability;

a digital memory connected to said iterative digital processing means, said digital memory storing the results of said separability computations;

an output display connected to said digital memory and said iterative digital processing means, said output display displaying results of said separability computations;

said iterative digital processing means including;

means for estimating probability density from the wavelet filtered profile data;

means for calculating likelihood ratio from said probability density estimates;

means for estimating a Bayes error employing resubstitution (R) and leave-one-out (L) processing; and

said output display being connected to said means for estimating said Bayes error, said output display displaying the Bayes error for data processed.

2. The apparatus of claim 1 wherein the wavelets in said library are selected for inclusion by having compact support.

3. The apparatus of claim 2 wherein the wavelets selected for inclusion in said library are wavelets having coefficients between 4 and 8.

4. The apparatus of claim 1 wherein said means for inputing a set of analog range profiles is a means for receiving and storing analog profiles of said targets.

5. The apparatus of claim 1 wherein said digital processing means for applying wavelets for digital filtering includes means for convolving said wavelets with said data.

6. The apparatus of claim 1 wherein said wavelets are Daubechies wavelets.

7. The apparatus of claim 1 wherein said means for estimating probability density is a KNN estimation process.

8. A computerized method of extracting spatial frequency featured in two sets of range profile data for two targets for a classification system using wavelets, comprising the steps of;

(1) assembling a library of wavelets having shapes, coefficients and computational efficiency consistent with the dictates of the application;

(2) inputing a set of analog range profiles for two targets;

(3) digitizing said analog range profiles for each of said two targets;

(4) selecting a wavelet from said library for use as a digital filter of said digitized range profiles;

(5) selecting a scale for use with said wavelet;

(6) using the first wavelet from said library at the first scale, digitally filter the two sets of digitized range profile data to produce a first filtered version of the original signal in each set at the first resolution;

(7) computing the separability of the data in the two sets of filtered range profile data and storing the results wherein said step of computing the separability of the two sets of filtered range profile data includes the steps of;

(a) estimating the probability density for each of the two sets of data;

(b) computing the likelihood ratio using said estimated probability densities; and

(c) estimating the Bayes error from a plot of KNN using leave one out (L) and resubstitution (R) methods;

(8) repeating steps 4 and 5 for each scale of the first wavelet;

(9) repeating steps 4, 5 and 6 for each wavelet in said library; and

(10) determining the best wavelet and scale for classifying the difference between the two sets of filtered range profile data.

9. The method of claim 8 wherein said step of assembling said library of wavelets includes the step of selecting said wavelets having compact support.

10. The method of claim 8 wherein said step of assembling said library of wavelets includes the step of selecting said wavelets from Daubechies wavelets having coefficients between 4 and 8.