11 RECONSTRUCTION METHODS.ppt

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