Image Reconstruction :Image Reconstruction By: Jessenia Ramirez Jessica Castillo Rotha Mam


Objectives :Define back projection Discuss ray sums Determine back projection techniques Discuss analytic reconstruction techniques Determine Fourier techniques Objectives


Back Projection :The back projection technique is a simple method of obtaining an approximate reconstruction from multiple projections It may be used in three forms: Graphically Photographically Electronically Back Projection


Cont’d :The back projection is a composite of all the ray sums of multiple angled to dimensional views such as those that may be acquired with a scintillation detector when projected on to an image field a such as computer matrix, film, or paper the overlap, a result of the rays sum projected at their respective angels represents a cross-section or a new plan of the original source Cont’d


Ray sums :Can best described if considered a point source acquired onto a 5x5 image matrix This point source can be given a value of 1and if back projected onto a new matrix the value of the point source would be placed in all the pixels representative of the angel of that acquisition Ray sums


Back Projection Technique :Is often referred to as a “brute force” It collects a source as a complete sum and projects it back as that sum to each pixel along the path of the acquired angel A point source collected and backprojected in this matter would built up an increased density where all the sums crossed and would present a representation of a new point source Back Projection Technique


Cont’d :A transaxial view is achieved by acquiring pre defined angulated views then projecting each view at the angle of data acquisition onto a matrix as a ray Cont’d


Analytic Reconstruction techniques :the most common method of removing the star artifact is using a filter Filtering may be obtained by the introduction of small negative values to each side of the peak in the ray histogram When these filtered views are reprojected the negative values will erase all but the highest portion of the ray sum Analytic Reconstruction techniques


2 Dimensional Fourier Reconstruction :A straight forward solution of the mathematical equation of reconstruction can be achieved by 2 dimensional Fourier reconstruction In order to understand the concept of Fourier transformation on must firs accept the data or counts per pixels this can be portrayed in both real space (the image) or in frequency space (wave forms ) 2 Dimensional Fourier Reconstruction


Fourier Transform Techniques :It lies in it’s straight forward analytic approach The simple application of an inverse Fourier transform technique can convert the recommended data into real space This transformation attempts a direct solution to equating observed value of transverse of direct distribution Fourier Transform Techniques


Applying it to SPECT :The long acquisition time and limited computer capacity of SPECT require the use of a faster filtered back projection technique Disadvantage of Fourier techniques The main problem is that the Fourier transform method cannot be applied until all projection have be acquired Applying it to SPECT


Iterative Methods of Reconstruction :Iterative Methods of Reconstruction Method or group of algorithms used to reconstruct 2D and 3D images from the projections of an object. There are many iterative algorithms, but they are all similar. Starts with an assumed image, computes projections from image, compares the original projection data and updates based upon the difference between the calculated and actual projections.


Actual Projection :Actual Projection


First estimate of image matrix :First estimate of image matrix


Second Projection :Second Projection Actual Image Compares to previous projection data Updates based on the difference between the calculated and actual projection Applying differences


Third Projection :Third Projection Previous projection Updated projection


Fourth Projection :Fourth Projection Previous projection Final Projection after numerous updates


Iterative Reconstruction :Iterative Reconstruction These process are repeated (hence, the term “iterative”) until all the projections have been updated giving you a final product. Our example included a 2 x 2 voxel, whereas actual reconstruction involves thousands of voxels with hundreds of projections that all need to be calculated and updated. This makes reconstruction slow because of the required computing power.


Iterative Reconstruction :Iterative Reconstruction


Iterative Reconstruction :Iterative Reconstruction PET scan reconstructed with ML-EM. (maximum-likelihood expectation-maximization)


Iterative Reconstruction :Iterative Reconstruction Shows a comparison between the filtered backprojection (top) and the ML-EM reconstruction (bottom) from the same dataset


Iterative Reconstruction :Iterative Reconstruction Comparison of EM reconstruction with FBP for different total counts. Note particular the streaking and noise appearance at low counts using FBP. Figures indicate the noise (standard deviation / mean) for a region in the liver.


Iterative Reconstruction :Iterative Reconstruction EM reconstruction of a simulated thorax illustrates the effect of iteration number on image quality and noise.


Photon Attenuation :Photon Attenuation γ-Ray photons are attenuated in body tissue while passing through a patient. The degree of attenuation depends on the photon energy, the thickness of tissue, and the linear attenuation coefficient of the photon in tissue. Photon attenuation makes it difficult to obtain accurate quantitative information about radiotracer uptake.


Attenuation Correction :Attenuation Correction Chang Method- an attenuation map is generated from individual pixel values based on the estimated thickness of an organ of interest and the assumption of a constant linear attenuation coefficient. Transmission Method- A transmission source mounted on the opposite side is used for data collection to correct for attenuation.


Attenuation Correction :Attenuation Correction Tomographic slices from a cardiac study reconstructed without attenuation correction on the top row and with attenuation correction on the bottom row. Note the more uniform distribution of radioactivity in the cardiac muscle depicted in the attenuation corrected images.


Attenuation Correction :Attenuation Correction Coronal slice of a whole body PET study, reconstructed without (left) and with (right) attenuation correction. The contours of the tumor and organs are less accurately defined in (left).


Reference :Image reconstruction packet Chang LT. A method for attenuation correction n radionuclide computed tomography. IEEE trans Nucl Sci 1978, NS 25:638-43 Herman GT. Image reconstruction from projections. New York: academic press, 1980 Reference


Question #1 :What is back projection? And what are the three forms it may be used in? Question #1


Answer #1 :technique is a simple method of obtaining an approximate reconstruction from multiple projections and it can be used graphically photographically, and electronically Answer #1


Question #2 :True or False? The back projection is a composite of all the ray sums of multiple angled to dimensional views such as those that may be acquired with a scintillation detector TRUE Question #2


Question #3 :Whatis another name for backprojection technique? Question #3


Answer #3 :Brute force Answer #3


Question #4 :What is the most common method of removing the star artifact? Question #4


Answer #4 :Is using a filter Answer #4


Question #5 :What is the disadvantage of using Fourier technique? Question #5


Answer #5 :The main problem is that the Fourier transform method cannot be applied until all projection have be acquired Answer #5


Question :Question What method of reconstruction involves repeated comparison and updating of projection data?


Answer :Answer Iterative Reconstruction


Question :Question What was the main disadvantage of iterative reconstruction discussed here?


Answer :Answer Reconstruction is slow because of the need of high computing power.


Question :Question What is the main reason of using any reconstruction technique?


Answer :Answer The construct a 3D image from a 2D image.


Question :Question Attenuation is generally not a problem in SPECT imaging. True or False?


Answer :Answer False, attenuation is a major problem in SPECT imaging.


Question :Question What two methods were discussed that are used for attenuation correction?


Answer :Answer Chang method and Transmission Method


#1 :The back projected image is A filtered, processed view B composite of all the ray sums C cross sectional view of the original D computer assisted transaxial view E b and c F b and d #1


Slide 49:E.b and c


#2 :A ray is best defined as A The imaging path B The overlap projection of a source C Density buildup of the counts D An even projection of the source along the path of acquired angle E C and d F None of the above #2


Slide 51:D. An even projection of the source along the path of acquired angle


#3 :The “star” effect can be created by A Improper source storage of the points B Produced from the overlapping of the ray sums C Septal penetration D Patient motion E None of the above F All of the above #3


Slide 53:B. Produced from the overlapping of the ray sums


#4 :Filtering A Cannot remove the star effect B Introduces a small negative value to the density C portion of the ray sum D Is basically different for each computer system E Will cancel or lose all but the highest density in the image F B and d G C and d #4


Slide 55:F. B and d


#5 :Data counts per pixel, can be portrayed A In frequency space B In a real space C In a series of sinusoidal D In a convoluted reflections image E A and b F A b and c #5


Slide 57:E. A and b


#6 :Fourier transformation A Transforms counts per pixel from frequency space into real space B Is limited by spatial resolution C Equates observed emission values with transverse distribution D Is limited by the imaging devices resolution E A and c F All the above #6


Slide 59:A. Transforms counts per pixel from frequency space into real spac


#7 :Attenuation A Is not a problem with SPECT B As a problem is diminished with SPECT, since multiple views are acquired C Correction methods must be used in SPECT because the measurements process mixes the activity distribution with the attenuating material D Compensation methods must be acquired to the raw data before reconstruction is performed E Is often demonstrated by an area increased activity or only appreciated on a high count study F C and e #7


Slide 61:B. As a problem is diminished with SPECT, since multiple views are acquired


#8 :Accurate quantitative information about radiopharmaceutical uptake is limited by A Patient motion B Dose restrictions C Exponential attenuation of photons by the patients body D A high count rate E B and c F C and d #8


Slide 63:F. C and d