Penalized-likelihood sinogram restoration for computed tomography

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

[1]  Jeffrey A. Fessler,et al.  Fast Monotonic Algorithms for Transmission Tomography , 1999, IEEE Trans. Medical Imaging.

[2]  Aziz Ikhlef,et al.  Crosstalk modeling of a CT detector , 2004, SPIE Medical Imaging.

[3]  Jerry L. Prince,et al.  Hierarchical reconstruction using geometry and sinogram restoration , 1993, IEEE Trans. Image Process..

[4]  Jeffrey A. Fessler,et al.  Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs , 1996, IEEE Trans. Image Process..

[5]  Jeffrey A. Fessler,et al.  Efficient and accurate likelihood for iterative image reconstruction in x-ray computed tomography , 2003, SPIE Medical Imaging.

[6]  Joseph A O'Sullivan,et al.  Prospects for quantitative computed tomography imaging in the presence of foreign metal bodies using statistical image reconstruction. , 2002, Medical physics.

[7]  Bruce R. Whiting,et al.  Signal statistics in x-ray computed tomography , 2002, SPIE Medical Imaging.

[8]  Alvaro R. De Pierro,et al.  A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography , 1995, IEEE Trans. Medical Imaging.

[9]  Jeffrey A. Fessler,et al.  Segmentation-free statistical image reconstruction for polyenergetic x-ray computed tomography with experimental validation , 2003 .

[10]  Xiaochuan Pan,et al.  Nonparametric regression sinogram smoothing using a roughness-penalized Poisson likelihood objective function , 2000, IEEE Transactions on Medical Imaging.

[11]  R. Carmi,et al.  Resolution enhancement of X-ray CT by spatial and temporal MLEM deconvolution correction , 2004, IEEE Symposium Conference Record Nuclear Science 2004..

[12]  Hakan Erdogan,et al.  Ordered subsets algorithms for transmission tomography. , 1999, Physics in medicine and biology.

[13]  Hongbing Lu,et al.  Nonlinear sinogram smoothing for low-dose X-ray CT , 2004 .

[14]  Patrick J. La Riviere Penalized‐likelihood sinogram smoothing for low‐dose CT , 2005 .

[15]  Jiang Hsieh,et al.  Computed Tomography: Principles, Design, Artifacts, and Recent Advances, Fourth Edition , 2022 .

[16]  R. White,et al.  Image recovery from data acquired with a charge-coupled-device camera. , 1993, Journal of the Optical Society of America. A, Optics and image science.

[17]  J. Hsieh,et al.  Investigation of a solid-state detector for advanced computed tomography , 2000, IEEE Transactions on Medical Imaging.

[18]  Ge Wang,et al.  Spiral CT image deblurring for cochlear implantation , 1998, IEEE Transactions on Medical Imaging.

[19]  W. Kalender,et al.  Generalized multi-dimensional adaptive filtering for conventional and spiral single-slice, multi-slice, and cone-beam CT. , 2001, Medical physics.

[20]  Hakan Erdogan,et al.  Monotonic algorithms for transmission tomography , 1999, IEEE Transactions on Medical Imaging.

[21]  Zhengrong Liang,et al.  Detector response restoration in image reconstruction of high resolution positron emission tomography , 1994, IEEE Trans. Medical Imaging.

[22]  J. Hsieh,et al.  An iterative approach to the beam hardening correction in cone beam CT. , 2000, Medical physics.

[23]  Chin-Tu Chen,et al.  A direct sinogram-restoration method for fast image reconstruction in compact DOI-PET systems , 2000 .

[24]  J. Hsieh Adaptive streak artifact reduction in computed tomography resulting from excessive x-ray photon noise. , 1998, Medical physics.

[25]  Miles N. Wernick,et al.  Image reconstruction for dynamic PET based on low-order approximation and restoration of the sinogram , 1997, IEEE Transactions on Medical Imaging.

[26]  C. Helstrom,et al.  Compensation for readout noise in CCD images , 1995 .

[27]  J. Fessler Statistical Image Reconstruction Methods for Transmission Tomography , 2000 .

[28]  Matthias Bertram,et al.  Potential of software-based scatter corrections in cone-beam volume CT , 2005, SPIE Medical Imaging.

[29]  R. Brooks,et al.  Beam hardening in X-ray reconstructive tomography , 1976 .

[30]  Randy Luhta,et al.  Design and performance of a 32-slice CT detector system using back-illuminated photodiodes , 2004, SPIE Medical Imaging.