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Proposed is a theoretically exact formula for inversion of data obtained by a spiral computed tomography (CT) scan with a two-dimensional detector array. The detector array is supposed to be of limited extent in the axial direction. The main property of the formula is that it can be implemented in a truly filtered backprojection fashion. First, one performs… (More)

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly-oriented copies of a molecule. The cryo-EM problem is to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct the 3D structure of the molecule. In some situations, the molecule under examination exhibits structural… (More)

We study a restriction of the Hilbert transform as an operator H T from L 2 (a 2 , a 4) to L 2 (a 1 , a 3) for real numbers a 1 < a 2 < a 3 < a 4. The operator H T arises in tomographic reconstruction from limited data, more precisely in the method of differentiated back-projection (DBP). There, the reconstruction requires recovering a family of… (More)

The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known sub-region in the ROI. In this paper, we improve a novel… (More)

The truncated Hilbert transform with overlap H T is an operator that arises in tomographic reconstruction from limited data, more precisely in the method of Differentiated Back-Projection (DBP). Recent work [1] has shown that the singular values of this operator accumulate at both zero and one. To better understand the properties of the operator and, in… (More)