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 ); decomposing indices r,θ of the collected projection array into a collection of subsets; utilizing an iterative loop to sequentially process each of the subsets, wherein a processing sequence of the subsets is determined based on an ordered subset criteria, and wherein the process includes: projecting the reconstructed image ƒ R ( x ) onto a calculated projection array p R (r,θ), wherein r,θ are indices for a current subset; calculating a comparison quantity q(r,θ), calculated from a calculated 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), wherein the comparison quantity is expressed as a ratio with a numerator term being expressed at least in part by a term that contains the collected projection array p(r,θ) and a denominator term being expressed at least in part by a term that contains reprojected data denoted by a calculated projection array p R (r,θ); generating a correction factor based on the correction array b( x ); generating a new reconstructed image ƒ R ( x ) that is modified from a previous reconstructed image by an operation involving the correction array b( x ); wherein the new reconstructed image is enhanced to a finer resolution; and wherein a smoothing operation is applied to a calculated projection array p R (r,θ); and outputting a final image ƒ R ( x ).