Chapter 5 - Image Reconstruction

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The image reconstruction process is based on the

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use of algorithms that uses the attenuation data measured by the detectors to systematically build up the image for viewing and interpretation

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Attenuation data collected from the CT detectors require

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mathematical algorithms to build the CT images for viewing and interpretation

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For computer to reconstruct an image of a patient by CT

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xray tube and detectors must rotate around the patient for at least 180 degrees and fan beam angle

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Dual Source CT scanners

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have 2 xray tubes and 2 detector arrays within gantry spaced at 90 degree angle

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Sufficient xray transmission values or attenuation data are

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collected to satisfy the image reconstruction process that builds up an image of acceptable quality

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Older CT scanners collected data over

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180 degrees

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Now they collect more

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attenuation data over 360 degrees to generate better quality images

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Understanding the basics of algorithms requires a basic into of the following concepts

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1. fourier transform

2. convolution

3. interpolation

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Algorithms

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a set of rules or directions for getting a specific output from a specific input

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All vagueness must be

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eliminated - distinguishing feature

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The rules must describe the operations that are so

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simple and well defined, they can be operated by machine

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Must terminate after

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a finite number of steps

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Fourier transform

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widely used in science and engineering

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The fourier transform is an

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analytic tool used to reconstruct images of a patient's anatomy in CT and MRI

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Fourier transform is a

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mathematical function that converts a signal in the spatial domain to a signal in the frequency domain

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The fourier transform divides a signal's

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waveform into a series of different frequencies and amplitudes which makes reconstruction of a CT image possible

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Convolution

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a digital image processing technique to modify images through a filter function

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Convolution involves

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multiplication of overlapping portion of the filter function and the detector response curve selectively to produce a 3rd function which is used for image reconstruction

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Interpolation

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a mathematical technique to estimate the value of a function from known values on either side of the function

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Interpolation is used in the

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CT image reconstruction process when dealing with spiral/helical CT slices

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Linear interpolation=

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simplest method of interpolation

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Ray

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straight path that the x-ray beam travels

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Ray sum

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measurement of the total x-ray absorption of a particular ray

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Projection

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a set of ray sums

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CT Problems

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calculating the attenuation coefficient distribution from all the ray sums of the multiple sets of obtained projections

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Reconstruction algorithms

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1. back projection

2. iterative algorithms

3. analytic methods - filtered back projection, fourier reconstruction

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Back projection

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summary of multiple projections to produce an image

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Back projection does not produce a

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sharp image of the object and therefore is not used in clinical CT

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Back projection is characterized by

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star pattern artifact

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Back projection is also called the

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summation method or linear superimposition method

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THe most striking artifact of back projection is the

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typical star pattern- occurs because points outside a high density object receive some of the back projected intensity of that object

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Can also be explained by a

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2x2 matrix, a computer can solve these equations quickly

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Iterative algorithms starts with

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an assumption and compares this assumption with measured values, makescorrections to bring the two into agreement, and then repeats this process overand over until the assumed and measured values are the same or withinacceptable limits”

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Iterative algorithms originally used by

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Hounsfield in the early years of CT but due to several limitations ofthe time period, iterative algorithms were not used initially in commercialscanners

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Iterative algorithms have resurfaced in

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manufactured CT scanners as of 2014 due to high-speed computinghaving overcome its earlier limitations while providing a reduction in imagenoise and minimizing radiation dose

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Analytic reconstruction algorithms

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Developedto overcome the limitations of back-projection and iterative algorithms

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Algorithm used in

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modern CT scanners

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Two types

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1. filtered back projection

2. fourier reconstruction algorithm

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Filtered back projection also known as

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convolution method

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Filtered back projection commonly

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used in CT systems today

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Common problems of filtered back projections

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¤Noise

¤Streakartifact

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Filtered back projection- projection profile

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filtered or convoluted to remove the typical starlike blurring that is characteristic of the simple back projection technique

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steps in Filtered back projection

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5

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1. all projection profiles

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obtained

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2. the logarithm of data

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obtained

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3. logarithmic values are

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multiplied by a digital filter, or convolution filter, to generate a set of filtered profiles

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4. the filtered profiles are then

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projected back

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5. the filtered projections are

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summed and the +/- components are canceled - which produces an image free of blurring

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Fourier reconstruction (definition)

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Theconversion of image information from the spatial domain to the frequencydomain, or vice versa

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Fourier reconstruction used in

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MRIbut not in modern CT because it requires more complicated mathematics than thefiltered back-projection algorithm

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Fourier reconstruction - a radiograph can be considered an image in the

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spatial domain - shades of gray represent various parts of anatomy (bone is white, air is black) in space

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With the fourier transform, this spatial domain image can be transformed into a

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frequency domain image

^this frequency domain image consists of a range of hight to low frequencies

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Fourier reconstruction technique does not use

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any filtering

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Advantages of fourier reconstruction - the image in the frequency domain can be

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manipulatedby changing the amplitudes of the frequency components

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A computer can

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perform manipulations - digital image processing

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Frequency info can be used to

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measure image quality through point spread function, line spread function and modulation transfer function

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Fourier slice theorem states

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the fourier transform of the projection of an object at an angle 0 is equal to a slice of the fourier transform of the object along angle 0

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Types of data - four types

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1. measurement data

2. raw data

3. convoluted data

4. image data

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Measurement Data - also referred to as

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scandata

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Measurement data- data that arise from the

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detectors

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Measurement data- these data require

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preprocessingcorrections before reconstruction algorithm is applied in order to prevent poorimage quality and artifacts

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These corrections are necessary because of errors in the measurement of data from

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1. beam hardening

2. adjustments for bad detector readings

3. scattered radiation

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If these errors are not corrected, they will cause

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1. poor image quality

2. generate image artifacts

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Raw data - resultant of

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preprocessedmeasurement data

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Raw data can be

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Storedand can be retrieved as needed

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Raw data are the result of

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preprocessed scan data and are subject to the image reconstruction algorithm used by the scanner

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Convoluted data -data that undergo the

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processof convolution technique

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Convolution is applying

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amathematical filter, kernel, to raw data

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Convolution removes

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blurring,thus improving image quality

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Convolution- raw data must be

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filtered first with a mathematical filter or kernel

^ this process is also referred to as the convolution technique

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Convolution kernels can only be applied to

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the raw data

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Image data - also known as

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reconstructed data

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Image data - convoluted data that have been

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back-projectedinto the image matrix to create CT images displayed on a monitor

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Image data- digital filters available

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1. standard algorithm

2. smoothing algorithm

3. edge enhancement algorithm

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Image data - various digital filters are available to

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suppress noise and improve detail

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Standard algorithm

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usually used before the previous algorithms, especially when a balance between noise and image detail is mandatory

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Smoothing algorithms

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reduce image noise and show good soft tissue anatomy - they are used in exams where soft tissue discrimination is important to visualize very low contrast structures

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Edge enhancement algorithms

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emphasize the edges of structures and improve detail but create image noise - they are used in exams in which fine detail is important, such as inner ear, bone structures, thin slice and fine pulmonary structures

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Image reconstruction in single slice spiral/helical CT

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Insingle-slice spiral/helical CT, interpolation is necessary prior to applying analgorithm, otherwise the reconstructed image would be blurred due to thepatient moving continuously through the gantry for a 360-degree rotation

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Interpolation is necessary before

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filter back projection is used

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A planar section must first be computed from the volume data set by using

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interpolation, after which images are generated with various interpolation algorithms

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Image reconstruction in Multislice spiral/helical CT - noteable difference between SSCT MSCT

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the latter uses multiple detector rows that cover a larger volume at an increased speed and therefore require new algorithms

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For CT Scanners with four detector rows, MSCT algorithms have been developed to allow for the

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reconstruction of variable slice thicknesses and address the problems of increased volume coverage and speed of the patient table

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Cone beam algorithms for MSCT scanners

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InMSCT scanners with four detector rows, the x-ray beam diverges at a cone anglereferred to as cone-beamgeometry

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SSCT scanners use

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wide fan beam geometries - image reconstruction algorithm based on interpolation followed by filtered back projection

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MSCT scanners with four detector rows use a

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wider fan beam geometry and use a 2D reconstruction with interpolation and 2 filtering, nown as z-interpolation algorithms

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ALgorithms for SSCT & MSCT with 4 detector rows are referred to as

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spiral/helical fan beam approximation algorithms- simply because they are based on the fan beam geometry

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For a 4 detector row MSCT scanner, the beam

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divergence from the x-ray tube to the outer edges of the detectors increases

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Such a beam is called a

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cone beam

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Within the cone beam, the rays that will be measured by the detectors are

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tilted at an angle relative to the central place (plane perpendicular to the long axis of the patient, z-axis) - this angle is called the cone angle

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Cone beam geometry- occurs when

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thex-ray beam diverges in a plane perpendicular to the long axis of the patient

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Cone angle increases as the

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numberof detector rows increases

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Largecone angle creates problem situations

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¤Inconsistentdata

¤Cone-beamartifacts

¤Decreasedimage quality

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Cone beam artifacts

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1. streaking

2. density changes

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Cone beam algorithms developed

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foruse in multislice CTscanners to improve accuracy and eliminate cone-beam artifacts

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Fan-beam algorithms are

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notapplicable nor accurate in multislice CT(MSCT) scanners because of the large cone angles

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Two classes of cone beam algorithms

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1. exact cone beam algorithms

2. approximate cone beam algorithms

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Algorithms used for 3D imaging are based from

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computergraphics and visual perception science

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3D algorithms allow the user to

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“interactively visualize, manipulate, and measure large 3D objects”

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3D imaging uses

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3D surface and volumetric reconstruction

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A 3D reconstruction technique for surface display is based on

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atleast 2 processes

1. preprocessing

2. display

and consists of the following operations

1. interpolation, 2. segmentation, 3. surface formation, 4. projection