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- Alexander Katsevich
- Physics in medicine and biology
- 2002

In this paper we continue studying a theoretically exact filtered backprojection inversion formula for cone beam spiral CT proposed earlier by the author. Our results show that if the phantom f is constant along the axial direction, the formula is equivalent to the 2D Radon transform inversion. Also, the inversion formula remains exact as spiral pitch goes… (More)

- Alexander Katsevich
- SIAM Journal of Applied Mathematics
- 2002

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)

Given a rather general weight function n 0 , we derive a new cone beam transform inversion formula. The derivation is explicitly based on Grangeat's formula (1990) and the classical 3D Radon transform inversion. The new formula is theoretically exact and is represented by a 2D integral. We show that if the source trajectory C is complete in the sense of Tuy… (More)

- Alexander Katsevich, Samit Basu, Jiang Hsieh
- Physics in medicine and biology
- 2004

We present an exact filtered backprojection reconstruction formula for helical cone beam computed tomography in which the pitch of the helix varies with time. We prove that the resulting algorithm, which is functionally identical to the constant pitch case, provides exact reconstruction provided that the projection of the helix onto the detector forms… (More)

- Gene Katsevich, Alexander Katsevich, Amit Singer
- SIAM J. Imaging Sciences
- 2015

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the… (More)

- E Katsevich, A Katsevich, G Wang
- Inverse problems
- 2012

In many practical applications, it is desirable to solve the interior problem of tomography without requiring knowledge of the attenuation function fa on an open set within the region of interest (ROI). It was proved recently that the interior problem has a unique solution if fa is assumed to be piecewise polynomial on the ROI. In this paper, we tackle the… (More)

We study a problem of locating and estimating singularities of a signal measured with noise on a discrete set of points (fixed-design model). The signal consists of a smooth part with bounded first derivative and of finite number of sin-gularities of the type (x − t i) p ± d i , 0 ≤ p ≤ 1 2. The case p = 0 corresponds to a piecewise continuous function. The… (More)

- Alexander Katsevich
- Physics in medicine and biology
- 2004

We propose an exact shift-invariant filtered backprojection algorithm for inversion of the cone beam data in the case when the source trajectory consists of an incomplete circle and a line segment. The algorithm allows for axial truncation of the cone beam data. The length of the line scan is determined only by the region of interest and is independent of… (More)

- Alexander Katsevich
- Physics in medicine and biology
- 2005

Proposed is an exact shift-invariant filtered backprojection algorithm for the circle-and-arc trajectory. The algorithm has several important features. First, it allows for the circle to be incomplete. Second, axial truncation of the cone beam data is allowed. Third, the length of the arc is determined only by the region of interest and is independent of… (More)

Proposed is a theoretically exact formula for inversion of data obtained by a spiral CT scan with a 2-D 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 shift-invariant filtering of a… (More)