Transcript Single-Photon emission computed tomography (SPECT )

Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering
• Filtering is a mathematical technique applied during reconstruction to improve
the appearance of the image.
• Filters have different types
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering
Domain of Images
Domain of Images
Spatial domain
• When image data is represented
in counts per pixel, this data is
said to be in spatial domain
• Filtering can be performed on this
data as it is but proves to be
computationally burdensome
Frequency domain
• This is when the data is represented as a
series of sine waves.
• The data is said to be transformed into
the frequency domain (fourier
transform)
• It is easier to perform filtering in this
domain
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering
Spatial and Frequency domains of Images
• These two domains are not entirely independent.
• In fact, they only represent different views of the underlying data
• The information obtained by the camera is not changed by this
transformation of the collected data from the spatial to the frequency
domain; all that is changed is the method of describing the data. more
generally, we can say that data can be transformed from one domain into
another with neither gain nor loss of the contained information.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
•
The only difference between simple and FBP is that in the latter method,
the profiles are modified by a reconstruction filter applied before they are
back-projected across the image.
• The filter has both positive and negative values. The negative portions of
the filtered profiles near the central peak “subtract out” some of the
projected intensity next to the peak.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
•
Kernal has negative values for
the peripheral pixels and a
positive value in the centre.
• This filter tends to enhance the
edges and reduce the intensity
of the star artifact
• A simple version of this filter is
with Kernal consists of central
value +2, surrounded by value
of -1.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
• This Kernal is sequentially
applied to each pixel of the
array.
• In the resulting array, the
outer values are zero or
negative
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
•
in a similar fashion, the
kernal is applied to the
second array of the example
in the figure.
• When these filtered arrays
are backprojected, their
peripheral negative values
cancel counts in a manner
that removes the portion of
the rays adjacent to the
image of the disk.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
• The relative
depression of
counts surrounding
the backprojected
disk helps to
separate it from the
background.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
• This figure is a graphic
representation of the
process
• The top panels
demonstrate the process
of back-projectiong
rectangles to create a
disk
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
• Each swipe of the paint
roller represents a ray.
• In the upper right image,
the combined rays
create a disk with
indistinct edges.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
• The bottom images demonstrate
the effect of a simple edge
enhancement filter in which
negative values are used to
border each rectangle prior to
backprojection (represented by
the small white squares on either
side of each rectangle)
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering data represented in the spatial domain in order to reduce star
artifacts (spatial filtering to reduce the star artifacts)
• These negative values cancel
contributions from adjacent raysums and the circle’s edge is seen
more clearly (bottom right).
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction (Simple and Filtered back projection)
Filtering
Types of filter
High-pass filter (Ex: ramp filter)
Low-pass filter (Ex: Hann, Hamming, Butterworth filters)
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
• Reconstruction is the process of creating trans-axial slices from
projection views.
• There are two basic approaches to creating the trans-axial slices.
1. Filtered backprojection
2. Iterative reconstruction
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
A relatively elegant technique called iterative reconstruction is steady replacing FBP
Images reconstructed with this technique exhibit significantly less star artifact than
those created using FBP
The algorithm approaches the true image, by means of successive approximations, or
estimate.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
• In iterative reconstruction, the computer
starts with an initial “guess”-estimate of
the data to produce a set of transaxial
slices
• Often the initial estimate is very simple,
such as a blank or uniform image.
• These slices are then used to create a
second set of projection views (using a
process called forward projection, which is
inverse of BP) which are compared to the
original projections views as acquired
from the patient.
It is performed by summing up the
intensities along the potential ray paths
for all projections through the estimated
image
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
• Unlikely that the initial estimate
closely resemble the true image
• the transaxial slices from the
computer’s estimate are then
modified using the difference
between, or ratio of, the two
sets of projections views.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
• A new set of transaxial slices
reconstructed from this
modified, or second, estimate
are then used to create a set of
projection views which are
compared to the original
projection views.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
• A gain these projection views
are compared to the original
projection views.
• If the process proceeds
efficiently, each iteration
generates a new set of
projection views that more
closely approximate the original
projection views.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
• The update-and-compare process is
repeated until the difference
between the forward-projected
profiles for the estimated image and
the actual recorded profiles falls
bellow some specified threshold
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
Simplified representation
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
Simplified representation
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
Simplified representation
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
Simplified representation
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
• In practice most iterative reconstruction are terminated at a predetermined number of iterations, that is, when the radiologists is satisfied
with the overall image quality, instead of allowing them to progress until
the difference between the estimated and projection views reaches a set
value.
• In general the image resolution improves with increasing number of
iterations . However, beyond a certain reasonable number of iterations,
further improvements in resolution can only be accomplished at the cost of
increased image noise.
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
The two basic components of iterative reconstruction algorithms are;
1. The method for comparing the estimated and actual profiles cost
function which measures the difference between the profiles generated
by forward projections through the estimated image and profiles actually
recorded from the scanned object
2. The method by which the image is updated on the basis of this
comparison the search or update function, which uses the output of
the cost function to update the estimated image
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction
• The general goal of algorithm development is to devise versions of these
functions that produce convergence of the estimated image toward the
true image as rapidly and accurately as possible.
• A number of methods have been developed to speed up these advanced
algorithms. One of the most popular is called ordered subsets expectation
maximization (OSEM)
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction (Adv)
Chapter-4
Single-Photon emission computed
tomography (SPECT)
Single-Photon emission computed tomography (SPECT)
Reconstruction
Iterative Reconstruction (disadva)