Alejandro Frangi, PhD Computational Imaging Lab Department of Information & Communication Technology Pompeu Fabra University www.cilab.upf.edu
X-ray Projection Imaging Computed Tomography Digital X-ray Imaging
The electromagnetic spectrum
Projection radiography Systems Chest X-rays, mammography Dental X-rays Fluoroscopy, angiography Properties High resolution Low dose Broad coverage Short exposure time
Projection radiography
Projection radiography Projection imaging is the acquisition of a 2D image of a patient s 3D anatomy Projection radiography is a transmission imaging procedure The optical density at any location on the film corresponds to the attenuation characteristics (e -mx ) of the patient at that location
Projection radiography Radiographic system
Projection radiography X-ray tube
Projection radiography X-ray tube Filament controls tube current (ma) Cathode and focusing cup Anode is switched to high potential 30-150 kv Tungsten Bremsstrahlung is 1% Heat is 99% Spins at 3200-3600 rpm Glass housing; vaccum
Projection radiography Cassette Light-tight tight and ensures screen contact with film Front surface - carbon fiber ID flash card area on back 1 or 2 Intensifying Screens Convert x-rays x to visible light Mounted on layers of compressed foam (produces force) Sheet of film Register the x-ray x distribution Chemically processed Storage and display
Projection radiography μ m (CS) μ m (PE) Tissue @ 26 kev Bone @ 35 kev Most radiographic interactions produce scattered photons Scattered photons violation of the basic principle of projection imaging: mis- information reducing contrast
Projection radiography Scatter-to to-primary ratio (S/P) Area of collimated x-ray x field Object thickness kvp of x-ray x beam
Projection radiography Loss of contrast In the absence of scatter: C 0 = [A-B]/A In the presence of scatter: C = C 0 x [1 / (1 + S/P)] S/P contrast 1/(1+{S/P}): contrast reduction factor
Projection radiography Antiscatter grid Between object and detector Uses geometry to scatter Thin lead septa separated by aluminum or carbon fiber Grid ratio (GR) = H/W = septa height/interspace width 8:1, 10:1 and 12:1 common, 5:1 for mammography GR S/P GR dose
Projection radiography
Image Formation from Projections
Projection-based image formation Image Formation from Projections The image formation process with external radiation sources: e.g. light for photography or X-ray for transmission imaging g( x) f ( α)
Image Formation from Projections Linear systems and impulse response: allows to give a general treatment to image formation { ( x) + ( x) } = { ( x) } + { ( x) } h ai bi ah I bh I General response function by superposition principle 1 2 1 2 f ( x) + f ( x) = h( x; α, g ( α)) + h( x; α, g ( α)) 1 2 1 2 If the system is linear the response does not depend on the intensity distribution f ( x) + f ( x) = h( x; α) g ( α) + h( x; α) g ( α) 1 2 1 2 General response function for a linear system by summing over the extent of the energy source f ( x) h( x; α) g( α) dα Source f ( x) = h( x α) g( α) dα = h g = If furthermore the response is spatially invariant Source PSF
Image Formation from Projections Radon Transform: Line integral projection P(p,θ) of the twodimensional Radon transform Rotating the (x, y) coordinate system by θ we obtain the (x, y ) coordinate system
Image Formation from Projections Radon Transform: Line integral projection P(p,θ) of the two-dimensional Radon transform
Image Formation from Projections Sinogram: image formed by all line integral projections P(p,θ)
Image Formation from Projections The Fourier slice theorem The Fourier transform of the Radon transform is The Fourier transform of the 2D signal g (x) is G (u,v) = G (u) Transforming into polar coordinates we have
Image Formation from Projections Fourier Slice Theorem
Image Formation from Projections Fourier Slice Theorem
Image Formation from Projections Back projection Intuitive idea: invert the Radon Transform from a finite set of projections
Image Formation from Projections Back projection The inverse Fourier transform After some manipulation
Image Formation from Projections Filtered back projection By applying the Fourier Slice Theorem, the inverse Fourier transform can be written With a weighting function
Image Formation from Projections Filtered back projection Each pixel is formed by integrating along all projection angles
Projection Based Image Formation Implementing a filtered back projection algorithm
Projection Based Image Formation Shepp and Logan Head phantom Consists of 10 ellipses Based on the linearity of the Radon Transform there is an analytical form of the P(r,θ)
Projection Based Image Formation Reconstruction of the Shepp and Logan Head phantom Increased number of projections
X-ray Computed Tomography Digital X-ray
X-ray Computed Tomography Scanning geometry Currently most X-ray CT scanners have an X-ray source with a fan beam geometry an a 360º ring of X-ray Detectors (~1000).
X-ray Computed Tomography CT Measurement Model Monoenergetic model Where E is the effective energy or the energy that in a given material will produce the same measured intensity in a monoenergetic source that in the actual polyenergetic source g d is the line integral of the attenuation coefficient at the effective energy Requires calibration measurement of Io
X-ray Computed Tomography Hounsfield units and tissue contrast Consistency across CT scanners desired CT number (Hounsfield units) is defined as: h has Hounsfield Units (HU) Usually rounded or truncated to nearest integer Range from -1000 to aprox + 3000 HU
X-ray Computed Tomography Hounsfield units and tissue contrast
X-ray Computed Tomography TUBE APERTURE With a weighting function DETECTORS
X-ray Computed Tomography
X-ray Computed Tomography
X-ray Computed Tomography
X-ray Computed Tomography
X-ray Computed Tomography X-ray emission in all directions X-ray tube Collimators Slice width Fan beam Detectors
X-ray Detectors There are two main types of detectors Ionization chambers the radiation liberates electrons from the gas atoms, creating positive charged ions Scintillation crystals make use of the property of certain chemical compounds to emit short light pulses after excitation by the passage of charged particles or by photons of high energy X-ray Computed Tomography Ionization chamber Photomultiplier tube
X-ray Computed Tomography
X-ray Computed Tomography Slip-ring technology Cine scanning (no table feed) CT fluoroscopy (several reconstruction per 360º) Spiral scanning (continuous table feed)
X-ray Computed Tomography
X-ray Computed Tomography
X-ray Computed Tomography
X-ray Computed Tomography
Digital X-ray Imaging Digital X-ray Imaging The imaged property is the attenuation coefficient μ but now only one projection Conventional systems had a very low efficiency which is nowadays improved with digital systems
Digital X-ray Imaging Digital X-ray Imaging The imaged property is the attenuation coefficient μ
Biplane & 3D Rotational Angiography Rotational angiography allows a 3D reconstruction based on dynamic X-raytype projection images