Method of image reconstruction for a filtered back projection in limited angle tomography

A calculating device for image reconstruction for a filtered back projection in limited angle tomography, the calculating device comprising

• a calculation unit configured to calculate a filter operator X determined non-iteratively as a generalized inverse operator (PB)+, wherein P consists of projection operators P1, P2, . . . , PN, with N denoting the complete projections described by data p, wherein P is represented in vector form as P=(P1, P2, . . . , PN)t, wherein B consists of back projection operators B1, B2, . . . BN, and wherein B is represented in vector form as B=(B1, B2, . . . , BN), where for every i Bi is the adjoint of Pi,
• wherein the calculation unit is configured to obtain limited angle tomography projection data p of an object O, wherein the radiation source is being moved relative to a detector when obtaining the projection data p,
• wherein the calculation unit is configured to calculate filtered projection data Xp upon applying the filter operator X on the obtained limited angle tomography projection data p in such a way that Xp describes N filtered projections of the object O and in such a way that each filtered projection is calculated from all N projections of the data p,
• wherein the calculation unit is configured to calculate a back projection B(Xp) of the filtered projection data Xp to generate a reconstructed image of the object O.