Patent ID: 8412468

Claim:
A method of pre-filtering and analyzing spectral data for the detection of elemental signatures in an interrogated object using multi-wavelet filters implemented on a computer having memory and one or more processors, comprising: electronically receiving into said memory data of gamma ray counts obtained from bombardment of an interrogated object; pre-filtering, utilizing said one or more processors, said data of gamma ray counts in order to maintain polynomial order using a quasi-interpolation pre-filter, said pre-filtering converting said data into pre-filtered signal data; generating, utilizing said one or more processors, an orthogonal scaling vector Φ=(φ 1 ,φ 2 ,φ 3 ,φ 4 ) T , wherein φ 1 , φ 2 , φ 3 , and φ 4 represent individual elements of said orthogonal scaling vector Φ, to construct filters for multi-wavelet decomposition of said pre-filtered signal data, said orthogonal scaling vector Φ=(φ 1 ,φ 2 ,φ 3 ,φ 4 ) T substantially satisfying a dilation equation defined by: Φ ⁡ ( x ) = 2 ⁢ ∑ i = - 2 1 ⁢ g i ⁢ Φ ⁡ ( 2 ⁢ x - i ) wherein g i represents matrix coefficients of said orthogonal scaling vector Φ, wherein i is a counter of a summation and represents whole numbers from −2 to 1, inclusive, and wherein x is an independent variable and represents real numbers, and having left boundary functions for φ 1 and φ 2 defined by: ϕ 1 L = ϕ 1 ⁢ R ⁢  [ 0 , 1 ] ⁢ - ( ϕ 1 ⁢  [ 0 , 1 ] ⁢ , ϕ 2  [ 0 , 1 ] ) ϕ 2 ⁢  [ 0 , 1 ] ⁢ , ϕ 2  [ 0 , 1 ] ⁢ ϕ 2  [ 0 , 1 ]  ϕ 1 ⁢  [ 0 , 1 ] ⁢ - ( ϕ 1 ⁢  [ 0 , 1 ] ⁢ , ϕ 2  [ 0 , 1 ] ) ϕ 2 ⁢  [ 0 , 1 ] ⁢ , ϕ 2  [ 0 , 1 ] ⁢ ϕ 2  [ 0 , 1 ]  ⁢ ⁢ and ⁢ ⁢ ϕ 2 L = 2 ⁢ ϕ 2 ⁢ ❘ [ 0 , 1 ] and right boundary functions for φ 1 and φ 2 defined by: φ 1 R ( x )=φ 1 L (1 −x ) and φ 2 R ( x )=−φ 2 L (1 −x ), constructing, utilizing said one or more processors, a multi-wavelet Ψ=(ψ 1 , ψ 2 , ψ 3 , ψ 4 ) T for said scaling vector Φ=(φ 1 ,φ 2 ,φ 3 ,φ 4 ) T , said multi-wavelet Ψ associated with said orthogonal scaling vector Φ=(φ 1 ,φ 2 ,φ 3 ,φ 4 ) T , wherein ψ 1 , ψ 2 , ψ 3 , and ψ 4 are individual elements of said multi-wavelet Ψ and substantially satisfy a dilation equation defined by: Ψ ⁡ ( x ) = 2 ⁢ ∑ i = - 2 1 ⁢ h i ⁢ Φ ⁡ ( 2 ⁢ x - i ) wherein h i represents matrix coefficients of Ψ, said multi-wavelet elements ψ 1 and ψ 2 having a left boundary dilation equation defined by: [ ψ 1 L ψ 2 L ] ⁢ ( x ) = h 0 L ⁡ [ ϕ 1 L ϕ 2 L ϕ 3 ϕ 4 ] ⁢ ( 2 ⁢ x ) + h 1 L ⁢ Φ ⁡ ( 2 ⁢ x - i ) and a right boundary dilation equation defined by: [ ψ 1 R ψ 2 R ] ⁢ ( x ) = h 0 R ⁢ Φ ⁡ ( 2 ⁢ x ) + h 1 R ⁢ Φ ⁡ ( 2 ⁢ x - 1 ) + h 2 R ⁡ [ ϕ 1 R ϕ 2 R ] ⁢ ( 2 ⁢ x - 1 ) ; ⁢ and interpolating, utilizing said one or more processors, said multi-wavelet Ψ for comparison with an elemental database to identify elements and element concentrations in said interrogated object.