Transcript Slide 1

IMAGE RECONSTRUCTION
ALGORITHM-A SET OF RULES
OR DIRECTIONS FOR
GETTING SPECIFIC OUTPUT
FROM SPECIFIC INPUT
ALGORITHM MUST
TERMINATE AFTER FINATE
NUMBER OF STEPS
DETECTORS
PRE-PROCESING
REFORMATTED RAW DATA
CONVOLUTION WITH FILTER
IMAGE RECONSTRUCTION ALGORITHM
IMAGE:
RECONSTRUCTED IMAGE
STORAGE
DISPLAY
RECORDING
ARCHIVING
HISTORY OF IMAGE
RECONSTRUCTION
• 1917 RADON DEVELOPED MATHEMATICAL SOLUTIONS TO
THE PROBLEM OF IMAGE RECONSTRUCTION FROM A SET OF
PROJECTIONS. UTILIZED IN SOLVING PROBLEMS IN
ASTRONOMY AND OPTICS.
• 1961 FINALLY THESE TECHNIQUES WERE USED IN
MEDICINE.
HOUNSFIELD’S IMAGES—NOISY
BECAUSE OF HIS RECONSTRUCTION
METHOD.
CONVOLUTION BACK PROJECTION
USED TO IMPROVE IMAGE QUALITY AND
SHORTEN PROCESSING TIME.
( USED BY Shepp & Logan)
ORIGINAL DATA
FILTERED DATA
CONVOLUTION BACK
PROJECTION DEVELOPED BY:
• RAMCHANDRAN
• LAKSHMINARAYANAN
BEAM GEOMETRIES AND DATA
ACQUSITION
• PARALLEL –SLOW
• FAN -FASTER
Algorithms applicable to CT
Back projection
Iterative methods
Analytic methods
BACK PROJECTION
• ALSO CALLED
SUMMATION
METHOD OR
LINEAR
SUPERPOSITION
METHOD
Example image of how a cube generates different
projections depending on the angle of projection
INCOMPLETE BACKPROJECTION
ITERATIVE ALGORITHMS
• SIMULTANEOUS ITERATIVE
RECONSTRUCTION TECHNIQUE
• ITERATIVE LEAST SQUARES
TECHNIQUE
• ALGEBRAIC RECONSTRUCTION
TECHNIQUE
ART USED BY HOUNSFIELD
IN HIS FIRST EMI BRAIN
SCANNER
ITERATIVE TECHNIQUES ARE
NOT USED IN TODAY’S
COMMERCIAL SCANNERS
ANALYTIC RECONSTRUCTION
ALGORITHMS
• FOURIER RECONSTRUCTION
• FILTERED BACK PROJECTION
USED IN MODERN CT SCANNERS
FILTERED BACK-PROJECTION
CONVOLUTION METHOD
• PROJECTION PROFILE IS FILTERED
OR CONVOLVED TO REMOVE THE
TYPICAL STAR LIKE BLURRING THAT IS
CHARACTERISTIC OF THE SIMPLE
BACK PROJECTION.
STEPS IN FILTERED BACK
PROJECTION
• ALL PROJECTION PROFILES ARE OBTAINED
• THE LOGARITHM OF DATA IS OBTAINED
• LOGARITHMIC VALUES ARE MULTIPLIED BY
DIGITAL FILTER
• FILTERED PROFILES ARE BACKPROJECTED
• THE FILTERED PROJECTIONS ARE SUMMED
AND THE NEGATIVE AND POSITIVE
COMPONENTS ARE CANCELLED
FOURIER RECONSTRUCTION
• USED IN MRI
• NOT USED IN CT BECAUSE OF
COMPLICATED MATHEMATICS
FOURIER TRANSFORM
• RADIOGRAPH –AN IMAGE IN SPATIAL
DOMAIN
• IN FOURIER TRANSFORM IMAGE IN
FREQUENCY DOMAIN
• CAN BE RETRANSFORMED BACK TO
SPATIAL DOMAIN BY WITH THE
INVERSE FOURIER
TYPES OF DATA
•
•
•
•
MEASUREMENT DATA
RAW DATA
CONVOLVED DATA
IMAGE DATA
MEASUREMENT DATA
(SCAN DATA)
• DATA THAT ARISES FROM
DETECTORS. IT NEEDS TO BE
PREPROCESSED TO ELIMINATE
ARTIFACTS.
RAW DATA
• IT’S THE RESULT OF SCAN DATA
BEING PRE-PROCESSED
CONVOLVED DATA
• FILTERED BACKPROJECTION IS THE
ALGORITHM USED BY MODERN CT.
• IT REQUIRES FILTERING AND THEN
BACKPROJECTION. RAW DATA IS
FILTERED USING MATHEMATICAL
FILTER OR KERNEL (CONVOLUTION)
• IT REMOVES BLURR. CONVOLUTION
CAN ONLY BE APPLIED TO RAW DATA.
IMAGE DATA
(RECONSTRUCTED DATA)
• CONVOLVED DATA THAT HAVE BEEN
BACKPROJECTED INTO THE IMAGE
MATRIX TO CREATE CT IMAGES
DISPLAYED ON THE MONITOR.
DETECTORS
SCAN DATA
PREPROCESSING
RAW DATA
CONVOLUTION
CONVOLVED DATA DATA
BACK
PROJECTION
ALGORITHM vs NOISE
DETAIL
EDGE-ENHANCEMENT
STANDARD
SMOOTHING
NOISE
RECONSTRUCTION IN SPIRAL
CT
• FILTERED BACK PROJECTION USED +
INTERPOLATION BACAUSE OF THE
CONTINUOUS MOVEMENT OF THE
PATIENT IN THE Z-DIRECTION.
( TO ELIMINATE MOTION BLURR)
RECONSTRUCTION IN
MULTISLICE SPIRAL CT
• INTERLACED SAMPLING
• LONGITUDINAL INTERPOLATION
• FAN BEAM RECONSTRUCTION
RECONSTRUCTION ALGORITHM
COMPARISON
• ANALYTIC METHODS ARE FASTER
THAN ITERATIVE ALGORITHMS.
• FILTERED BACK PROJECTION IS USED
IN MODERN CT SCANNERS