Expectation Maximization and Filtered Back Projection are two common techniques for Tomographic reconstruction of images and volumes. While papers often demonstrat that EM produces higher quality reconstructions, particularly from lower numbers of projections, FBP remains popular due to its low computational complexity. In the following work we present and analyse a modified Expectation Maximiz...

In this paper we present forward and backward projection formulae for catadioptric omnidirectional vision using an arbitrarily located cone mirror and perspective camera. For the back projection a quasi closed-form solution is derived, while for the forward projection an itterative method is used. We then show that these formulae can be used to achieve stereo vision using only a single mirror, ...

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the co...

The iterative reconstruction (IR) algorithms are able to generate CT images with higher quality compared with the filtered backprojection method when the projection data is noisy or the radiation dose is low. IR can also be used when the data is incomplete. The major disadvantage of the IR is its high demand on computation and slow reconstruction. To improve the time performance of the IR we pa...

The objective of this paper is to investigate a new non-iterative paradigm for image reconstruction based on the use of nonlinear back projection filters. This method, which we call nonlinear back projection (NBP), attempts to directly model the optimal inverse operator through off-line training. Potential advantages of the NBP method include the ability to better account for effects of limited...

We propose the Learned Primal-Dual algorithm for tomographic reconstruction. The algorithm accounts for a (possibly non-linear) forward operator in a deep neural network by unrolling a proximal primal-dual optimization method, but where the proximal operators have been replaced with convolutional neural networks. The algorithm is trained end-to-end, working directly from raw measured data and i...

In this paper, we demonstrate that image reconstruction can be expressed in terms of neural networks. We show that filtered backprojection can be mapped identically onto a deep neural network architecture. As for the case of iterative reconstruction, the straight forward realization as matrix multiplication is not feasible. Thus, we propose to compute the back-projection layer efficiently as fi...