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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)

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)

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)

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)

| 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 o f the formula is that it can be implemented in a truly ltered backprojection fashion. First, one performs shift-invariant ltering of a… (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)

A 3π algorithm is obtained in which all the derivatives are confined to a detector array. Distance weighting of backprojection coefficients of the algorithm is studied. A numerical experiment indicates that avoiding differentiation along the source trajectory improves spatial resolution. Another numerical experiment shows that the terms depending on the… (More)