Patent ID: 7110606

Claim:
A method performed by a computer for encoding a one-dimensional (1-D) image signal x(t), the image signal being a periodic signal with period N=nτ, where n is an integer and τ is a fixed positive integer, the method comprising: defining a 1-D cubic-spline filter r(t) by r ⁡ ( t ) = { ( 3 / 2 ) ⁢  t  3 - ( 5 / 2 ) ⁢  t  2 + 1 , 0 ≤  t  < 1 - ( 1 / 2 ) ⁢  t  3 + ( 5 / 2 ) ⁢  t  2 - 4 ⁢  t  + 2 , 1 ≤  t  < 2 ; 0 , 2 ≤  t  ; ( 1 ) applying the filter to the image signal x(t) with y j = ∑ t = - 2 ⁢ ⁢ τ + 1 2 ⁢ ⁢ τ + 1 ⁢ r ⁡ ( t ) ⁢ ⁢ x ⁡ ( t + j ⁢ ⁢ τ ) , 0 ≤ j ≤ n - 1 , ( 3 ) to compute y j where y j is an n-point circular correlation of filter r(t) and image signal x(t); computing a cyclic matrix of size n×n B=[b 0 ,b 1 , . . . ,b n−1 ] C , where matrix coefficients b k are the autocorrelation coefficients for 0≦k≦n−1 between two filters r(t) and r(t+kτ), b k = ∑ t = - 2 ⁢ ⁢ τ + 1 2 ⁢ ⁢ τ + 1 ⁢ r ⁡ ( t ) ⁢ ⁢ r ⁡ ( t + k ⁢ ⁢ τ ) . 0 ≤ k ≤ n - 1 ( 4 ) and where for τ+2, b 0 =α=1.641, b 1 =b n−1 =β=0.246, b 2 =b n−2 =γ=−0.07, b 3 =b n−3 =δ=0.004, b 4=0 , b 5=0 , . . . , b n−4 =0; computing a reconstructed filter by computing inverse matrix of B, A=B −1 , where the reconstructed filter A is a circular matrix of size n×n, where A=[a 0 ,a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 , . . . ,a n−6 ,a n−5 ,a n−4 ,a n−3 ,a n−2 ,a n−1 ] C (6) and where the coefficients of the reconstructed filter A are a 0 =0.646, a 1 =a n−1 =−0.109, a 2 =a n−2 =0.0467, a 3 =a n−3 =−0.014, a 4 =a n−4 =0.0046, a 5 =a n−5 =−0.00148, and a 6 ≅a 7 ≅a 8 ≅ . . . ≅a n−6 ≅0; and computing X=B −1 Y=AY (7) where Y=[y 0 ,y 1 , . . . ,y n−1 ] T is tranpose of row vector Y and X=[x 0 ,x 1 , . . . ,x n−1 ] T is transpose of the row vector X, by computing a circular convolution: x j = ∑ k = 0 n - 1 ⁢ y k ⁢ ⁢ a ( j - k ) n , ( 8 ) where x j are convolution coefficients between time samples y k and a k for 0≦k,j≦n−1 and are the encoded values of the image signal x(t) at sampling points and where (j−k) n denotes a residue (j−k) module n.