1. Image reconstruction method for reconstructing a tomographic image (f j ) of a region of investigation within an object, comprising the steps of: providing detector data (y i ) comprising Poisson random values measured at an i-th of a plurality of different positions relative to the object, providing a predetermined system matrix A ij assigning a j-th voxel of the object to the i-th detector data (y i ), wherein the system matrix A ij defines the detector data (v i ) as linear combinations of the original object data and is determined by geometric or physical features of an imaging device used for collecting said detector data (y i ) and reconstructing the tomographic image (f j ) based on the detector data (y i ), said reconstructing step including a procedure of minimizing a functional F(f) depending on the detector data (y i ) and the system matrix A ij and additionally including a sparse or compressive representation of the object in an orthobasis T, wherein the tomographic image (f j ) represents a global minimum of the functional F(f).