A tomographic image generation apparatus for generating an image of an object, the image generation apparatus comprising: - a measured projection values providing unit for providing measured projection values of the object, - a reconstruction unit for reconstructing the image based on the provided measured projection values such that costs defined by a cost function are iteratively reduced, wherein the cost function depends on differences between calculated projection values, which have been determined by simulating a forward projection through the image, and the provided measured projection values, and characterised in that a degree of dependence of the cost function on a respective difference depends on the respective difference such that the cost function depends less on a first respective difference than it depends on a second respective difference which is smaller than the first respective difference, thereby considering an amount of the respective differences, whereby when a respective difference is relatively large the cost function depends less on this respective difference, whereby when a respective difference is relatively small the cost function depends stronger on this respective difference, thereby considering a degree of disturbance of a measured projection value by motion and/or by an incomplete illumination and improving image quality, or characterised in that the cost function depends on parameters calculated for sets of differences based on the differences included in the sets of differences, the degree of dependence of the cost function on a parameter for a respective set of differences depending on the parameter such that the cost function depends less on a parameter for a first set of differences than it depends on a parameter for a second set of differences, which is smaller than the parameter for the first set of differences, thereby considering, thereby considering an amount of the respective differences, whereby when a respective difference is relatively large the cost function depends less on this respective difference, whereby when a respective difference is relatively small the cost function depends stronger on this respective difference, thereby considering a degree of disturbance of a measured projection value by motion and/or by an incomplete illumination and improving image quality. - a measured projection values providing unit for providing measured projection values of the object, - a reconstruction unit for reconstructing the image based on the provided measured projection values such that costs defined by a cost function are iteratively reduced, wherein the cost function depends on differences between calculated projection values, which have been determined by simulating a forward projection through the image, and the provided measured projection values, and characterised in that a degree of dependence of the cost function on a respective difference depends on the respective difference such that the cost function depends less on a first respective difference than it depends on a second respective difference which is smaller than the first respective difference, thereby considering an amount of the respective differences, whereby when a respective difference is relatively large the cost function depends less on this respective difference, whereby when a respective difference is relatively small the cost function depends stronger on this respective difference, thereby considering a degree of disturbance of a measured projection value by motion and/or by an incomplete illumination and improving image quality, or characterised in that the cost function depends on parameters calculated for sets of differences based on the differences included in the sets of differences, the degree of dependence of the cost function on a parameter for a respective set of differences depending on the parameter such that the cost function depends less on a parameter for a first set of differences than it depends on a parameter for a second set of differences, which is smaller than the parameter for the first set of differences, thereby considering, thereby considering an amount of the respective differences, whereby when a respective difference is relatively large the cost function depends less on this respective difference, whereby when a respective difference is relatively small the cost function depends stronger on this respective difference, thereby considering a degree of disturbance of a measured projection value by motion and/or by an incomplete illumination and improving image quality.