1. A method for generating a three-dimensional image of a scanned object from a plurality of cone-beam projections passed through the object and attenuated thereby, the method comprising: a) positioning the source at an initial position on a predetermined scan path; b) passing a projection of cone-beam radiation comprising a plurality of projection rays from a common focal point through an object, the cone-beam projection being attenuated by partial absorption in the object; c) detecting radiation intensity of the attenuated cone-beam projection on an area detector; d) obtaining a two-dimensional attenuation image of the cone-beam projection from the detected radiation intensity; e) obtaining an intermediate transform function from the two-dimensional attenuation image on a set of planes passing through the focal point; f) at least once, repositioning the source and repeating steps (b)-(e); g) filtering the intermediate transform functions acquired from consecutive attenuation images at two or more source positions using a moving-frame technique to obtain the second-order radial derivative of the Radon transform; h) backprojecting the second-order radial derivative of the Radon transform in a two-dimensional space along each projection ray to generate an intermediate, locally reconstructed, three-dimensional image with constant values assigned along each projection ray; i) at least once, repeating steps (f)-(h); and j) summing the plurality of intermediate, locally reconstructed, three-dimensional images obtained for the plurality of cone-beam projections to obtain an ultimate, reconstructed, three-dimensional image of the object.