Image Reconstruction

Image Reconstruction

With tomosynthesis technique, two-dimensional projection images are acquired first. Reconstruction algorithms are designed to achieve three-dimensional image volume. A few image reconstruction algorithms have been investigated by various research groups, including Niklason’s image stretching method [4], back projection (BP) reconstruction algorithm, filtered back projection (FBP) algorithm, maximum likelihood expectation maximization (MLEM), matrix inversion tomosynthesis (MITS), simultaneous algebraic reconstruction techniques (SART), tuned-aperture computed tomography (TACT) reconstruction methods, etc. FBP and MITS apply deblurring algorithms to enhance the contrast and sharpness so increase the conspicuity. MLEM acquires the reconstruction results by maximizing the likelihood with the measured projection images on the detector and assuming Poisson distribution model. SART solve the liner equations of x-ray attenuation.

Shift-And-Add (SAA) algorithm was the common mathematical reconstruction algorithm, and it lines up each projection image in term of its relative shift amount to acquire the reconstructed slice at the specified depth. Back-Projection reconstruction (BP) is quite similar, but it improves the image quality of the reconstructed volume by taking into account shift amounts of each pixel location on every reconstructed slice. Many reconstruction algorithms take SAA and BP as their foundation for further deblurring . Both MITS and FBP are fast-speed reconstruction methods with enhanced image contrast and sharpness with deblurring algorithms to remove out-of-plane blur: FBP applied filters to reconstruct from transformed projection images, and MITS used SAA to compute matrix inversion deblurring of each reconstructed slice.

MLEM and SART are time-consuming methods with large size of the breast image volume. Both of them compute the attenuation when the projection line passes through the voxel in reconstruction volume. Ray-tracing method was used to calculate the length of the path when the projection line penetrates the voxel.

Please refer to my papers:
W. Zhou, X. Qian, J. Lu, O. Zhou, Y. Chen, Multi-beam x-ray source breast tomosynthesis reconstruction with different algorithms, SPIE 2010.
Y. Chen, W. Zhou, G. Yang, J. Lu and O. Zhou, Breast tomosynthesis reconstruction with a multi-beam x-ray source, SPIE 2009.