Helical cone-beam computed tomography image reconstruction algorithm for a tilted gantry with N-PI data acquisition

We present a cone-beam image reconstruction algorithm for helical CT scanning with a tilted gantry and N-PI data acquisition. When the gantry is tilted, the effective source trajectory in the patient's reference frame lies on an elliptical cylinder, rather than on a circular cylinder as in the standard helical scanning mode. The aim of this work is to provide a means of reconstructing an image object directly from cone-beam projection data without transforming the image object into a virtual object and without rebinning projection data acquired for a real object into the projection data of the virtual object. This task has been accomplished by the application of an exact reconstruction algorithm, which utilizes an important geometrical property of the elliptical helical trajectory: the existence of generalized N-PI lines for a given image point. Based on this property, a mathematically exact image reconstruction scheme via filtering the backprojection image of differentiated projection data (FBPD) is applied to solve the reconstruction problem. Due to the gantry tilt, the required detector size is different from that of the standard helical trajectory (nontilted). A systematic analysis of the required detector size is presented. For an N-PI data acquisition scheme, an image may be reconstructed using data from an N-PI window, an (N?2)-PI window, and so on. Although the images reconstructed using an N-PI (N>1) window are noisier than the images reconstructed from a 1-PI window, a weighted-average scheme over reconstructed images is presented to generate a final image with significantly lower noise variance than that in the 1-PI data acquisition scheme. The image reconstruction algorithm was numerically validated using a mathematical phantom.

[1]  A. Katsevich.  On two versions of a 3π algorithm for spiral CT , 2004 .

[2]  R. Proksa,et al.  A quasiexact reconstruction algorithm for helical CT using a 3-Pi acquisition. , 2003, Medical physics.

[3]  S. Samarasekera,et al.  Exact cone beam CT with a spiral scan. , 1998, Physics in medicine and biology.

[4]  W A Kalender,et al.  Advanced single-slice rebinning for tilted spiral cone-beam CT. , 2001, Medical physics.

[5]  Rolf Clackdoyle,et al.  Cone-beam reconstruction using the backprojection of locally filtered projections , 2005, IEEE Transactions on Medical Imaging.

[6]  Hiroyuki Kudo,et al.  General reconstruction theory for multislice X-ray computed tomography with a gantry tilt , 2004, IEEE Transactions on Medical Imaging.

[7]  Katsuyuki Taguchi,et al.  Tilted helical Feldkamp cone-beam reconstruction algorithm for multislice CT , 2003, SPIE Medical Imaging.

[8]  Ge Wang,et al.  PI-line-based image reconstruction in helical cone-beam computed tomography with a variable pitch. , 2005, Medical physics.

[9]  Xiaochuan Pan,et al.  Exact image reconstruction on PI-lines from minimum data in helical cone-beam CT. , 2004, Physics in medicine and biology.

[10]  V. Hutson.  Integral Equations , 1967, Nature.

[11]  Emil Y. Sidky,et al.  Exact image reconstruction from n-PI acquisition data in helical cone-beam CT , 2005, SPIE Medical Imaging.

[12]  Frédéric Noo,et al.  Exact helical reconstruction using native cone-beam geometries. , 2003, Physics in medicine and biology.

[13]  M. Defrise,et al.  A solution to the long-object problem in helical cone-beam tomography. , 2000, Physics in medicine and biology.

[14]  Hengyong Yu,et al.  Exact BPF and FBP algorithms for nonstandard saddle curves. , 2005, Medical physics.

[15]  S. Leng,et al.  Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data , 2004, Physics in medicine and biology.

[16]  Thomas Köhler,et al.  EnPiT: filtered back-projection algorithm for helical CT using an n-Pi acquisition , 2005, IEEE Transactions on Medical Imaging.

[17]  A. Katsevich.  Analysis of an exact inversion algorithm for spiral cone-beam CT. , 2002, Physics in medicine and biology.

[18]  Alexander Katsevich,et al.  Theoretically Exact Filtered Backprojection-Type Inversion Algorithm for Spiral CT , 2002, SIAM J. Appl. Math..

[19]  Xiaochuan Pan,et al.  Image reconstruction on PI-lines by use of filtered backprojection in helical cone-beam CT. , 2004, Physics in medicine and biology.

[20]  Michael Grass,et al.  The n-PI-method for helical cone-beam CT , 2000, IEEE Transactions on Medical Imaging.

[21]  Xiaochuan Pan,et al.  An extended data function and its generalized backprojection for image reconstruction in helical cone-beam CT. , 2004, Physics in medicine and biology.

[22]  Hengyong Yu,et al.  A unified framework for exact cone-beam reconstruction formulas. , 2005, Medical physics.

[23]  Hengyong Yu,et al.  A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an n-PI-window , 2005, Physics in medicine and biology.

[24]  M. Glas,et al.  Principles of Computerized Tomographic Imaging , 2000 .

[25]  J. Hsieh.  Tomographic reconstruction for tilted helical multislice CT , 2000, IEEE Trans. Medical Imaging.

[26]  A. Katsevich,et al.  Exact filtered backprojection reconstruction for dynamic pitch helical cone beam computed tomography. , 2004, Physics in medicine and biology.

[27]  E. Sidky,et al.  Minimum data image reconstruction algorithms with shift-invariant filtering for helical, cone-beam CT , 2005, Physics in medicine and biology.