1. A method for reconstructing an image implemented on a computing system, comprising: inputting a collected projection array p(r, θ) produced from a computed tomography (CT) system imaging an object defined with a multi-dimensional image function ƒ( x ); generating an initial reconstructed image ƒ R ( x ); utilizing an iterative loop to perform: projecting the reconstructed image ƒ R ( x ) onto a projection array p R (r, θ); calculating a comparison quantity q(r, θ), calculated from the projection array p R (r, θ) and the collected projection array p(r, θ); backprojecting onto a correction array b( x ) a function that utilizes the comparison quantity q(r, θ); generating a correction factor based on the correction array b( x ); generating a new reconstructed image ƒ R ( x ) that modifies a previous reconstructed image with an operation involving the correction array b( x ); wherein a spatial sampling of pixels in the new reconstructed image is enhanced to a finer resolution; and wherein a smoothing operation is applied to the projection array p R (r, θ); and outputting a final image ƒ R ( x ).