Method and device for digital x-ray tomosynthesis. Tomographic and/or three-dimensional images of an object are obtained with an x-ray source and a digital x-ray image sensor. The source, object and sensor are positioned relative to each other and attenuation data is obtained for a large number of rays of x-radiation through the object. A special algorithm is provided to convert the data into images. To calculate the images the algorithm uses iterative processes with a least squares type technique but with generalized (as opposed to specific) functions. The algorithm solves for the functions which are the images. Preferred embodiments include a system having an x-ray point source with a cone of diverging x-rays, a two-dimensional digital x-ray image sensor, two linear translation stages to independently move both the x-ray source and the digital x-ray image sensor, two rotation mechanisms to rotate the two linear translation stages, a microprocessor to control the data acquisition, and a computer programmed with a special algorithm to calculate the tomographic images. A plurality of sets of digital data (representing x-ray algorithm images of an object) are acquired by the digital x-ray image sensor, with the x-ray source and the digital x-ray image sensor located at different positions and angles relative to the object. The digital data representing the x-ray attenuation images is stored in the computer. Special mathematical algorithms then compute multiple images of the object using the acquired digital data. These images could include multiple tomographic images, a three-dimensional image, or a multiple three-dimensional images.