Penalized-likelihood sinogram restoration for computed tomography

Abstract

We formulate computed tomography (CT) sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. CT measurement data are degraded by a number of factors-including beam hardening and off-focal radiation-that produce artifacts in reconstructed images unless properly corrected. Currently, such effects are addressed by a sequence of sinogram-preprocessing steps, including deconvolution corrections for off-focal radiation, that have the potential to amplify noise. Noise itself is generally mitigated through apodization of the reconstruction kernel, which effectively ignores the measurement statistics, although in high-noise situations adaptive filtering methods that loosely model data statistics are sometimes applied. As an alternative, we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function. We consider three different strategies for estimating the set of ideal line integrals, one based on direct estimation of ideal "monochromatic" line integrals that have been corrected for single-material beam hardening, one based on estimation of ideal "polychromatic" line integrals that can be readily mapped to monochromatic line integrals, and one based on estimation of ideal transmitted intensities, from which ideal, monochromatic line integrals can be readily estimated. The first two approaches involve maximization of a penalized Poisson-likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares (PWLS) objective applied in the transmitted intensity domain. We find that at low exposure levels typical of those being considered for screening CT, the Poisson-likelihood based approaches outperform the PWLS objective as well as a standard approach based on adaptive filtering followed by deconvolution. At higher exposure levels, the approaches all perform similarly.

Achieving Routine Submillisievert CT Scanning: Report from the Summit on Management of Radiation Dose in CT

“…Some of these techniques are already commercially available, including automatic exposure control (10)(11)(12), automatic tube potential selection (13), beam-shaping filters, and dynamic z-axis collimators (14,15). Others, such as iterative reconstruction algorithms and noise reduction methods, are just becoming widely available (16)(17)(18)(19)(20)(21)(22)(23). Together, these techniques can reduce dose by a factor of two to four (Table).…”

Adaptive filtered-back-projection for computed tomography

“…To account for photon counting errors, the measurements y are modeled as realizations of random variables y ∼ Poisson I 0 e −(Rf ) , where (Rf ) = μ(x 1 , x 2 )dl is the Radon transform of μ at line and I 0 is X-ray intensity of the source. This is a simplified statistical model for transmission tomography scan, which can be extended to account for many physical phenomena [12]. As seen, the variance of the resulting Poisson noise depends on the initial X-ray intensity as well as on the scanned object.…”

“…A sinogram correction before the application of FBP is also considered and practiced for improved reconstruction [12,9]. In [12], the sinogram is restored by iteratively optimizing a statistically based penalty function.…”

Projection space denoising with bilateral filtering and CT noise modeling for dose reduction in CT

“…[3][4][5][6][7][8][9][10] In conventional shift-invariant filtration applied during image reconstruction, the suppression of the high-frequency component in the sinogram is performed with a simple assumption that all the measurements are equally reliable, which may result in severe degradation of spatial resolution. [3][4][5][6][7][8] More sophisticated methods have been developed to adap-tively smooth the data by taking into account the local statistics in the measurements.…”

“…6,7 Other approaches model CT noise in a more complete way, including compound Poisson, off-focal, cross-talk, and other effects. 8,9 Iterative reconstruction methods can achieve significant denoising but at the expense of very long computation times. 10 Techniques based entirely on image space have also been described, taking advantage of the image structure to smooth noise while preserving edges but suffering from the complicated properties of noise in image space in CT. [11][12][13] In this work, we investigated a locally adaptive method for noise control in CT.…”