Fan-beam reconstruction algorithm for a spatially varying focal length collimator

Abstract

Fan-beam collimators are used in single-photon-emission computed tomography (SPECT) to improve the sensitivity for imaging of small organs. The disadvantage of fan-beam collimation is the truncation of projection data surrounding the organ of interest or, in those cases of imaging large patients, of the organ itself, producing reconstruction artifacts. A spatially varying focal length fan-beam collimator has been proposed to eliminate the truncation problem and to maintain good sensitivity for the organ of interest. The collimator is constructed so that the shortest focal lengths are located at the center of the collimator and the longest focal length is located at the periphery. The focal length is assumed to increase monotonically toward the edge of the collimator. A reconstruction algorithm for this type of fan-beam collimation, expressed as an infinite series of convolutions followed by one backprojection, is presented. Simulations show that only a small number of N terms in the series is needed to obtain high-quality reconstructions. Computer simulations showed that if the focal length function is smooth, the reconstructions are free of artifacts.

Image reconstruction with a shift‐variant filtration in circular cone‐beam CT

“…As a result, the filtration is employed directly on the measured data without data conversion and the spatial resolution properties can thus be retained. For example, collimators with spatially varying focal lengths are usually used in SPECT to increase the sensitivity for imaging small organs (Cao and Tsui, 1994;Hsieh, 1989;Zeng et al, 1993), data acquired with such collimators are not in the form of fan-, coneor parallel-beam data. To use existing standard reconstruction algorithms, a rebinning process is generally necessary to convert the acquired emission data to a desired form.…”

List-mode data reconstruction via the finite Hilbert transform of the derivative of the backprojection

“…Equations (9) and (10) are reduced to , (11) . (12) Similarly, this method can be extended to the fan-beam imaging geometry with an equally spaced detector [7], the varying focal length fan-beam geometry [11][12][13][14] and fanbeam geometry with a non-circular detector orbit in SPECT (single photon emission computed tomograhy).…”

Small field-of-view cardiac SPECT can be implemented on hybrid SPECT/CT platforms where data acquisition and reconstruction are guided by CT

“…Gullberg et al [10] introduced a reconstruction algorithm to correct for ring artifacts from image truncation when performing cone beam tomography of the heart. Zeng et al [11,12] discuss the use of fan-beam and cone-beam collimators with varying focal lengths to minimize the effects of truncation. A new reconstruction algorithm was developed for such a collimator and has shown promise in reducing truncation artifacts.…”