Abstract: An image reconstruction method for reconstructing an image fmin representing a region of investigation within an object includes providing detector data (yi) having Poisson random values from an X-ray transmission measurement using an X-ray source and a detector device, the detector data (yi) being measured at an i-th of a plurality of different pixel positions of the detector device relative to the object, and reconstructing the image fmin based on the detector data (yi), the reconstructing step including a procedure of minimizing a functional F ? ( f _ ) = 1 k ? ? i = 1 k ? ? ( ? i - y i ? log ? ? ? i ) + a ? ? T - 1 ? f _ ? p where f is a current test image used for minimizing the functional F(f). The image fmin represents the global minimum of F(f).

Abstract: An image reconstruction method for reconstructing an image fmin representing a region of investigation within an object includes providing detector data (yi) having Poisson random values from an X-ray transmission measurement using an X-ray source and a detector device, the detector data (yi) being measured at an i-th of a plurality of different pixel positions of the detector device relative to the object, and reconstructing the image fmin based on the detector data (yi), the reconstructing step including a procedure of minimizing a functional F ? ( f _ ) = 1 k ? ? i = 1 k ? ? ( ? i - y i ? log ? ? ? i ) + a ? ? T - 1 ? f _ ? p where f is a current test image used for minimizing the functional F(f). The image fmin represents the global minimum of F(f).

Abstract: An image reconstruction method for reconstructing a tomographic image (fj) of a region of investigation within an object (1), comprises the steps of providing detector data (yi) comprising Poisson random values measured at an i-th of a plurality of different positions, e.g. i=(k,l) with pixel index k on a detector device and angular index l referring to both the angular position (?l) and the rotation radius (rl) of the detector device (10) relative to the object (1), providing a predetermined system matrix Aij assigning a j-th voxel of the object (1) to the i-th detector data (yi), and reconstructing the tomographic image (fj) based on the detector data (yi), said reconstructing step including a procedure of minimizing a functional F(f) depending on the detector data (yi) and the system matrix Aij and additionally including a sparse or compressive representation of the object (1) in an orthobasis T, wherein the tomographic image (fj) represents the global minimum of the functional F(f).

Abstract: An image reconstruction method for reconstructing a tomographic image (fj) of a region of investigation within an object (1), comprises the steps of providing detector data (yi) comprising Poisson random values measured at an i-th of a plurality of different positions, e.g. i=(k,l) with pixel index k on a detector device and angular index l referring to both the angular position (?l) and the rotation radius (rl) of the detector device (10) relative to the object (1), providing a predetermined system matrix Aij assigning a j-th voxel of the object (1) to the i-th detector data (yi), and reconstructing the tomographic image (fj) based on the detector data (yi), said reconstructing step including a procedure of minimizing a functional F(f) depending on the detector data (yi) and the system matrix Aij and additionally including a sparse or compressive representation of the object (1) in an orthobasis T, wherein the tomographic image (fj) represents the global minimum of the functional F(f).