11 reconstruction methods.ppt
TRANSCRIPT
IMAGE RECONSTRUCTION
ALGORITHM-A SET OF RULES OR DIRECTIONS FOR GETTING SPECIFIC OUTPUT
FROM SPECIFIC INPUT
ALGORITHM MUST TERMINATE AFTER FINATE
NUMBER OF STEPS
PRE-PROCESING
REFORMATTED RAW DATA
CONVOLUTION WITH FILTER
IMAGE RECONSTRUCTION ALGORITHM
RECONSTRUCTED IMAGE
IMAGE:IMAGE:
STORAGEDISPLAY
RECORDINGARCHIVING
DETECTORS
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 BACK-PROJECTION
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-PROJECTIONCONVOLUTION 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
BACKPROJECTION
ALGORITHM vs NOISEDETAIL
NOISE
STANDARD
SMOOTHING
EDGE-ENHANCEMENT
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