Disclosed are methods and systems for tomographic reconstructing of desired image data from image data corresponding to a plurality of detector images comprising compressing the plurality of detector images, identifying a projection matrix which describes an ideal way in which an object under study is projected onto a detector, computing a modified projection matrix as a function of the projection matrix and a compression technique utilized in compressing the plurality of detected images, and reconstructing a compressed representation of the desired image data from the compressed detector images and the modified projection matrix, using an iterative linear systems solver.