Image reconstruction method for reconstructing an image f min representing a region of investigation within an object, comprising the steps of: - providing detector data (y i) comprising Poisson random values from an X-ray CT imaging of the object using an X-ray source and a detector device, said 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 f min based on the detector data (y i), wherein the image f min is a volumetric reconstruction of the object, said reconstructing step including a procedure of minimizing a functional F(f) F f ̲ = 1 k ∑ i = 1 k μ i − y i log μ i + a T − 1 f ̲ p wherein f is a current test image used for minimizing the functional F( f), 1 k ∑ i = 1 k μ i − y i log μ i is a maximum-likelihood risk functional for Poisson statistics, said parameters μi being transmission projections of the test image f, said projections being computed according to Beer-Lambert's law at the i -th pixel position relative to the X-ray source, |T -1 f | p is a sparsity enforcing functional including the lp norm of vector T - 1 f with 0≤ p <2, said vector T -1 f being a sparse or compressive representation of f in a (bi-) orthogonal basis T, and a is a calibration factor, wherein - the image f min represents the global minimum of the functional F(f), and - the parameters μi are μ i = ∑ i ′ B ′ ii ′ I 0 exp − ∑ j A i ′ j f j + r wherein B ' ii ' is a matrix representing a response function of the detector device assigning an i '-th spatial position on the detector surface to the i-th detector data ( y i), I 0 is an intensity of the unattenuated X ray beam, A i ' j is a predetermined system matrix assigning a j -th voxel of the object to the i '-th spatial position on the detector surface, and r is a background count parameter of the detector device. - providing detector data (y i) comprising Poisson random values from an X-ray CT imaging of the object using an X-ray source and a detector device, said 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 f min based on the detector data (y i), wherein the image f min is a volumetric reconstruction of the object, said reconstructing step including a procedure of minimizing a functional F(f) F f ̲ = 1 k ∑ i = 1 k μ i − y i log μ i + a T − 1 f ̲ p wherein f is a current test image used for minimizing the functional F( f), 1 k ∑ i = 1 k μ i − y i log μ i is a maximum-likelihood risk functional for Poisson statistics, said parameters μi being transmission projections of the test image f, said projections being computed according to Beer-Lambert's law at the i -th pixel position relative to the X-ray source, |T -1 f | p is a sparsity enforcing functional including the lp norm of vector T - 1 f with 0≤ p <2, said vector T -1 f being a sparse or compressive representation of f in a (bi-) orthogonal basis T, and a is a calibration factor, wherein f is a current test image used for minimizing the functional F( f), 1 k ∑ i = 1 k μ i − y i log μ i is a maximum-likelihood risk functional for Poisson statistics, said parameters μi being transmission projections of the test image f, said projections being computed according to Beer-Lambert's law at the i -th pixel position relative to the X-ray source, |T -1 f | p is a sparsity enforcing functional including the lp norm of vector T - 1 f with 0≤ p <2, said vector T -1 f being a sparse or compressive representation of f in a (bi-) orthogonal basis T, and a is a calibration factor, wherein - the image f min represents the global minimum of the functional F(f), and - the parameters μi are μ i = ∑ i ′ B ′ ii ′ I 0 exp − ∑ j A i ′ j f j + r wherein B ' ii ' is a matrix representing a response function of the detector device assigning an i '-th spatial position on the detector surface to the i-th detector data ( y i), I 0 is an intensity of the unattenuated X ray beam, A i ' j is a predetermined system matrix assigning a j -th voxel of the object to the i '-th spatial position on the detector surface, and r is a background count parameter of the detector device. wherein B ' ii ' is a matrix representing a response function of the detector device assigning an i '-th spatial position on the detector surface to the i-th detector data ( y i), I 0 is an intensity of the unattenuated X ray beam, A i ' j is a predetermined system matrix assigning a j -th voxel of the object to the i '-th spatial position on the detector surface, and r is a background count parameter of the detector device.