Patent ID: 7496619

Claim:
A method for recovering information about an object of interest ƒ from a data set {f(x j )} obtained from nonuniform data sample points x j εX, j being an indexing number, X representing the set of points where the object of interest ƒ is sampled, comprising the steps of: a. selecting data ƒ(x j ) from the data set {ƒ(x j )}; b. constructing an approximation operator Q X ; c. applying the approximation operator Q X to the data ƒ(x j ) to obtain an approximation Q X ƒ(x j ); d. constructing a projection operator P; e. applying the projection operator P to the approximation Q X ƒ(x j ) to obtain a first approximations ƒ 1 =P Q X ƒ(x j ); f. obtaining an error e=ƒ(x j )−ƒ 1 ; g. applying the projection operator P to the error e to obtain a first approximation of error e 1 =P e; h. obtaining a second approximations ƒ 2 =ƒ 1 +e 1 ; i. returning to step (e) until a sequence ƒ n =ƒ 1 +e 1 +e 2 +e 3 +AAA+e n−1 is obtained, wherein function ƒ n converges to the object of interest ƒ; and j. outputting the obtained sequence ƒ n , wherein the outputting step comprises at least one step of: (A) displaying the obtained sequence ƒ n in a display with a GUI; (B) storing the obtained sequence ƒ n in the computer readable medium, a memory device, or a network device; (C) transmitting the obtained sequence ƒ n over network to a network device; and (D) printing the obtained sequence ƒ n in a printer.