a method and apparatus are provided for three dimensional computerized tomographic imaging of an object , wherein cone beam energy from a cone beam source is applied to at least a portion of an object to be imaged by causing relative rotational motion between the source and the object at a plurality of source positions along a path scanning trajectory . an area detector receives cone beam energy from the source on a plurality of detector elements arranged in an array of rows and columns , so that its detector elements develop a set of measurement signals at each of the plurality of source positions . derivative radon transform data is directly developing by multiplication of the measurement signals of each set by pre - calculated and stored weight factors . thereafter , an image of the object is reconstructed using the directly developed radon derivative data .