System for extracting targets from radar signatures

Claim 3

The method of claim 1 wherein said step of decomposing further comprises the steps of: forming a Basis of said scaling basis coefficients for each said Scale ##EQU17## representing said high resolution profile radar signal in subspace {V j :=0,1,2, . . . } using ##EQU18## forming a Basis of said wavelet basis coefficients for each said Scale ##EQU19## representing said high resolution profile radar signal in subspace {O j :j=0,1,2, . . . } using ##EQU20##

Claim 4

The method of claim 1 wherein said neural network uses said wavelet basis coefficients as the input data to said neural network and further comprises a layered backpropagation neural network, said layered backpropagation neural network having an input neuron for each said wavelet basis coefficient.

Claim 5

The method of claim 1 further comprising the step of computing the Variance of said wavelet basis coefficients at each said Scale, said step of computing said Variance precedes said step of estimating the fractal dimension.

Claim 6

The method of claim 4 wherein said step of decomposing further comprises the steps of: forming a Basis of said scaling basis coefficients for each said Scale ##EQU21## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU22## and forming a Basis of said wavelet basis coefficients for each said Scale ##EQU23## representing said high resolution profile radar signal in subspace {O j :j=0,1,2, . . . } using ##EQU24##

Claim 7

The method of claim 4 wherein said step of computing said Variance further comprises the following equation: ##EQU25## where m j is the mean of said wavelet basis coefficients at said Scale j.

Claim 8

The method of claim 4 wherein said neural network uses said Variance of said wavelet basis coefficients as the input data to said neural network and further comprises a layered backpropagation neural network, said layered backpropagation neural network having an input neuron for each said Variance of said wavelet basis coefficients at each said Scale.

Claim 9

Apparatus for estimating the fractal dimension of the image for an artificial object's fractal surface, comprising: a radar system; means for receiving radar return signals reflected from the artificial object's fractal surface; means for combining said return signals with frequency stepped pulse signals consisting of a train of N pulses, where N is the number of frequency steps, to produce detected pulse return signals; means for applying a Fourier Transform to said detected pulse return signals to produce a high resolution profile signal; means for decomposing said high resolution profile signal into Scales of scaling basis coefficients and wavelet basis coefficients using a pyramid transform in conjunction a Discrete Wavelet Transform to calculate said scaling basis coefficients and said wavelet basis coefficients; and means for estimating the fractal dimension of the artificial object's fractal surface with a neural network.

Claim 10

Apparatus for estimating the fractal dimension of the image for an artificial object's fractal surface, comprising: a radar system; means for receiving radar return signals reflected from the artificial object's fractal surface; means for combining said return signals with frequency stepped pulse signals consisting of a train of N pulses, where N is the number of frequency steps, to produce detected pulse return signals; means for applying a Fourier Transform to said detected pulse return signals to produce a high resolution profile signal; means for decomposing said high resolution profile signal into Scales of scaling basis coefficients and wavelet basis coefficients using a pyramid transform in conjunction a Discrete Wavelet Transform to calculate said scaling basis coefficients and said wavelet basis coefficients; and means for estimating the fractal dimension of the artificial object's fractal surface with a neural network.

Claim 11

The apparatus of claim 8 wherein said means for decomposing further comprises: means for forming a Basis of said scaling basis coefficients for each said Scale ##EQU26## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU27## and means for forming a Basis of said wavelet basis coefficients for each said Scale ##EQU28## representing said high resolution profile radar signal in subspace {O j :j=0,1,2, . . . } using ##EQU29##

Claim 12

The apparatus of claim 8 wherein said neural network uses said wavelet basis coefficients as the input data to said neural network and further comprises a layered backpropagation neural network, said layered backpropagation neural network having an input neuron for each said wavelet basis coefficient.

Claim 13

The apparatus of claim 8 further comprising means for computing the Variance of said wavelet basis coefficients at each said Scale.

Claim 14

The apparatus of claim 11 wherein said means for decomposing further comprises: means for forming a Basis of said scaling basis coefficients for each said Scale ##EQU30## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU31## and means for forming a Basis of said wavelet basis coefficients for each said Scale ##EQU32## representing said high resolution profile radar signal in subspace {O j :j=0,1,2, . . . } using ##EQU33##

Claim 15

The apparatus of claim 11 wherein said means for computing said Variance further comprises the following equation: ##EQU34## where m j is the mean of said wavelet basis coefficients at said Scale j.

Claim 16

The apparatus of claim 11 wherein said neural network uses said Variance of said wavelet basis coefficients as the input data to said neural network and further comprises a layered backpropagation neural network, said layered backpropagation neural network having an input neuron for each said Variance of said wavelet basis coefficients at each said Scale.

Claim 19

The method of claim 15 wherein said detected pulse return signals include coherently detected pulse return signals.

Claim 20

The method of claim 15 wherein said detected pulse return signals include incoherently detected pulse return signals.

Claim 23

The method of claim 18 wherein said detected pulse return signals include coherently detected pulse return signals.

Claim 24

The method of claim 18 wherein said detected pulse return signals include incoherently detected pulse return signals.

Claim 25

Apparatus for estimating the fractal dimension of the radar signature for a target's fractal surface, comprising: a high resolution radar; means for aiming said high resolution radar at the target; means for transmitting frequency stepped pulse signals consisting of a train of N pulses through said high resolution radar where N is the number of frequency steps; means for receiving return signals from said high resolution radar, said return signals reflected from the target's fractal surface; means for combining said return signals with said frequency stepped train of pulses to produce detected pulse return signals; means for applying a Fourier Transform to said detected pulse return signals to produce a high resolution profile radar signal; means for decomposing said high resolution profile radar signal into Scales of scaling basis coefficients and wavelet basis coefficients using a pyramid transform in conjunction with a Discrete Wavelet Transform to form a Basis of said scaling basis coefficients for each said Scale ##EQU44## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU45## and and form a Basis of said wavelet basis coefficients for each said Scale ##EQU46## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU47## means for estimating the fractal dimension of the target's fractal surface with a layered backpropagation neural network using said wavelet basis coefficients as the input data to said neural network, said neural network having an input neuron for each said wavelet basis coefficient.

Claim 26

Apparatus for estimating the fractal dimension of the radar signature for a target's fractal surface, comprising: a high resolution radar; means for aiming said high resolution radar at the target; means for transmitting frequency stepped pulse signals consisting of a train of N pulses through said high resolution radar where N is the number of frequency steps; means for receiving return signals from said high resolution radar, said return signals reflected from the target's fractal surface; means for combining said return signals with said frequency stepped train of pulses to produce detected pulse return signals; means for applying a Fourier Transform to said detected pulse return signals to produce a high resolution profile radar signal; means for decomposing said high resolution profile radar signal into Scales of scaling basis coefficients and wavelet basis coefficients using a pyramid transform in conjunction with a Discrete Wavelet Transform to form a Basis of said scaling basis coefficients for each said Scale ##EQU44## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU45## and and form a Basis of said wavelet basis coefficients for each said Scale ##EQU46## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU47## means for estimating the fractal dimension of the target's fractal surface with a layered backpropagation neural network using said wavelet basis coefficients as the input data to said neural network, said neural network having an input neuron for each said wavelet basis coefficient.

Claim 27

The apparatus of claim 21 wherein said detected pulse return signals include coherently detected pulse return signals.

Claim 28

The apparatus of claim 21 wherein said detected pulse return signals include incoherently detected pulse return signals.

Claim 29

Apparatus for estimating the fractal dimension of the radar signature for a target's fractal surface, comprising: a high resolution radar; means for aiming said high resolution radar at the target; means for transmitting frequency stepped pulse signals consisting of a train of N pulses through said high resolution radar where N is the number of frequency steps; means for receiving return signals from said high resolution radar, said return signals reflected from the target's fractal surface; means for combining said return signals with said frequency stepped train of pulses to produce detected pulse return signals; means for applying a Fourier Transform to said detected pulse return signals to produce a high resolution profile radar signal; means for decomposing said high resolution profile radar signal into Scales of scaling basis coefficients and wavelet basis coefficients using a pyramid transform in conjunction with a Discrete Wavelet Transform to form a Basis of said scaling basis coefficients for each said Scale ##EQU48## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU49## and and form a Basis of said wavelet basis coefficients for each said Scale ##EQU50## representing said high resolution profile radar signal in subspace {O j :j=0,1,2, . . . } using ##EQU51## means for computing the Variance of said wavelet basis coefficients at each said Scale using the following equation: ##EQU52## where m j is the mean of said wavelet basis coefficients at said scale j; and means for estimating the fractal dimension of the target's fractal surface with a layered backpropagation neural network using said Variance of said wavelet basis coefficients as the input data to said neural network, said neural network having an input neuron for each said Variance of said wavelet basis coefficients at each said Scale.

Claim 30

Apparatus for estimating the fractal dimension of the radar signature for a target's fractal surface, comprising: a high resolution radar; means for aiming said high resolution radar at the target; means for transmitting frequency stepped pulse signals consisting of a train of N pulses through said high resolution radar where N is the number of frequency steps; means for receiving return signals from said high resolution radar, said return signals reflected from the target's fractal surface; means for combining said return signals with said frequency stepped train of pulses to produce detected pulse return signals; means for applying a Fourier Transform to said detected pulse return signals to produce a high resolution profile radar signal; means for decomposing said high resolution profile radar signal into Scales of scaling basis coefficients and wavelet basis coefficients using a pyramid transform in conjunction with a Discrete Wavelet Transform to form a Basis of said scaling basis coefficients for each said Scale ##EQU48## representing said high resolution profile radar signal in subspace {V j :j=0,1,2, . . . } using ##EQU49## and and form a Basis of said wavelet basis coefficients for each said Scale ##EQU50## representing said high resolution profile radar signal in subspace {O j :j=0,1,2, . . . } using ##EQU51## means for computing the Variance of said wavelet basis coefficients at each said Scale using the following equation: ##EQU52## where m j is the mean of said wavelet basis coefficients at said scale j; and means for estimating the fractal dimension of the target's fractal surface with a layered backpropagation neural network using said Variance of said wavelet basis coefficients as the input data to said neural network, said neural network having an input neuron for each said Variance of said wavelet basis coefficients at each said Scale.

Claim 31

The apparatus of claim 24 wherein said detected pulse return signals include coherently detected pulse return signals.

Claim 32

The apparatus of claim 24 wherein said detected pulse return signals include incoherently detected pulse return signals.