Patent ID: 8630466

Claim:
An image processing method for providing a digitized image as an approximation of an image function ƒ, wherein the digitized image comprises a plurality of pixels with a predetermined pixel size, comprising the steps of: providing the image function ƒ from Radon data comprising a plurality of projection functions measured corresponding to a plurality of predetermined projection directions (v), wherein the projection functions comprise discrete projection profiles, each discrete projection profile comprising projection values γ (v, j) corresponding to a plurality of projection lines (j) with the same projection direction (v), wherein j and v are non-negative integers, wherein the image function ƒ can be represented as a projection sum A 2 ⁢ ⁢ m ⁡ ( f ; x , y ) = ∑ v = 0 2 ⁢ m ⁢ ∑ k = 0 2 ⁢ m ⁢ S k , v ⁢ U k ⁡ ( x ⁢ ⁢ cos ⁢ ⁢ ϕ v + y ⁢ ⁢ sin ⁢ ⁢ ϕ v ) , wherein x and y are spatial coordinates and k and m are non-negative integers, S k , v = k + 1 ( 2 ⁢ m + 1 ) 2 ⁢ ∑ j = 0 2 ⁢ m ⁢ γ j , v ⁢ sin ⁡ ( k + 1 ) ⁢ ( 2 ⁢ γ + 1 ) ⁢ π 4 ⁢ m + 2 , ϕ v = 2 ⁢ v ⁢ ⁢ π 2 ⁢ m + 1 ⁢ ⁢ and ⁢ ⁢ U k are orthogonal ridge polynomials, and the image function ƒ is determined in an image reconstruction processor by the steps of: determining an intermediate sum ∑ k = 0 2 ⁢ m ⁢ S k , v ⁢ sin ⁡ ( k + 1 ) ⁢ θ v , wherein θ v =arccos(x cos φ v +y sin φ v )) with a Sinus Transform procedure, and determining the projection sum as A 2 ⁢ m ⁡ ( f ; x , y ) = ∑ v = 0 2 ⁢ m ⁢ 1 sin ⁢ ⁢ θ v ⁡ ( x , y ) ⁢ ∑ k = 0 2 ⁢ m ⁢ S k , v ⁢ sin ⁡ ( k + 1 ) ⁢ θ v , and determining pixel values from the image function, the pixel values representing the digitized image to be obtained, wherein the pixel values are determined in dependence on at least two image function values within the pixel size of the respective pixel.