1. A method for reconstruction of an image and for compensating for motion of a dynamically deforming object to be imaged by providing a reconstructed image of the object, comprising: acquiring projection data of the object using a scanner; calculating, by a controller, motion vector field data for the object to estimate a motion of the object; reconstructing, by the controller, the acquired projection data utilizing an image reconstruction methodology; and generating, by the controller, the reconstructed image based on the reconstructed projection data and the calculated motion vector field data, wherein the image reconstruction methodology includes steps of: a) defining a region-of-interest (ROI) and a set of Hilbert lines such that every point inside the ROI lies on only one Hilbert line, and all line integral projection data passing through any object point on each Hilbert line are measured, b) along each Hilbert line, computing a derivative backprojection to obtain a Hilbert transformed image, c) along each Hilbert line, inverting the Hilbert transformed image to obtain a function, and d) reconstructing a finite set of images at a reference time using the steps a)-c) to compensate for a time-dependent affine transformation and applying a weighted summation to the finite set of images using the following equation: f 0 ⁡ ( x t ) = ∑ m = 1 M ⁢ W 0 , m ⁡ ( x t ) ⁢ f 0 , m ⁡ ( x t ) / ∑ m = 1 M ⁢ W 0 , m ⁡ ( x t ) , where f o,m is the finite set of images at the reference time, and W o,m is a spatially varying weight which corresponds to spatially changing elements of affine transformation.