1 / 15

Tomographic Image Reconstruction

Tomographic Image Reconstruction. Dr. Rajeev Srivastava. Overview. Image creation Image reconstruction Brute force Iterative techniques Backprojection Filtered backprojection. Image Creation. Tomogram image of a slice taken through a 3D volume. Projection

gsiniard
Download Presentation

Tomographic Image Reconstruction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Tomographic Image Reconstruction Dr. Rajeev Srivastava

  2. Overview • Image creation • Image reconstruction • Brute force • Iterative techniques • Backprojection • Filtered backprojection

  3. Image Creation • Tomogram • image of a slice taken through a 3D volume • Projection • Attenuation profile through the object • The projection function represents the summation of the attenuation coefficients along a given X-ray path

  4. Image Creation • Sinogram • 2D data set – result of stacking all the projections together • Radon transform • Transformation of a function (image) into the sinogram, p(r) • Computes projections of an image along specified directions

  5. Image Reconstruction • Process of estimating an image from a set of projections • Several algorithms exist to accomplish this task: • Brute force • Iterative techniques • Backprojection • Filtered backprojection

  6. Brute Force • projection set defines a system of simultaneous linear equations - can be solved using algorithms from linear algebra • not practical for real systems (can have hundreds of simultaneous equations for a single slice)

  7. Iterative Reconstruction • Known as algebraic reconstruction technique – ART, consists of three steps: • Make an initial guess at the solution • Compute projections based on the guess • Refine the guess based on the weighted difference between the actual projections and the desired projections • Original reconstruction method used in medical imaging • Works, but is slow and susceptible to noise

  8. Backprojection • Propagates sinogram back into the image space along the projection paths (inverse Radon transform) • Backprojection image is a blurred version of the original image • The projection theorem (central slice theorem) - provides an answer to inverse Radon transform problem • Set of 1D Fourier transform of the Radon transform of a function is the 2D Fourier transform of that function

  9. Fourier Reconstruction • Calculate the 1D Fourier transform of all projections [p(r) = P(k)] • Place P(k) on polar grid to get P(k,) • Resample in Cartesian space to get F(kx,ky) • Calculate the 2D inverse Fourier transform of F(kx,ky) to get f(x,y) – image • Resultant image is noisy

  10. Fourier Reconstruction

  11. Filtered Backprojection • Take projections - sinogram • Transform data to the frequency domain • Filter data • Inverse transform – smoothed sinogram • Backproject

  12. Filtered Backprojection

  13. Filtered Backprojection • ramp filter + nearest neighbor algorithm • ramp & Hamming filter + nearest neighbor algorithm • ramp filter + linear interpolation • ramp & Hamming filter + linear interpolation 2 1 4 3

  14. References • Image Processing: The Core of Nuclear Cardiology, Scott M. Leonard, MS, CNMT, Northwestern University, ppt presentation • Xiang Li , Jun Ni and Ge Wang, Parallel iterative cone beam CT image reconstruction on a PC cluster, Journal of X-Ray Science and Technology 13 (2005) 63–72 • HARISH P. HlRlYANNAlAH, X-ray Computed Tomography for Medical Imaging, IEEE SIGNAL PROCESSING MAGAZINE

  15. Thank you

More Related