database-assisted low-dose ct image restoration klaus mueller computer science lab for visual...
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Database-Assisted Low-Dose CT Image
Restoration
Klaus MuellerComputer Science
Lab for Visual Analytics and Imaging (VAI)
Stony Brook University
Wei Xu, Sungsoo Ha and Klaus Mueller
Motivation
Minimize the radiation, while maximize the clarity
Enforce better quality directly in the reconstruction process
• TV-CBCT [J. Xun & S. Jiang]
• ASD-POCS [E. Sidky & X. Pan]
• R-OS-SIRT [W. Xu & K. Mueller]
Solutions
Improve quality in a post-processing de-noising step
• [Z. Kelm et al.]
• [H. Yu & G. Wang]
• [J. Ma & Z. Liang]
• [W. Xu & K. Mueller]
Post-processing De-noising Filter - NLM
Neighborhood filters – Non-local Means (NLM)
• To update pixel x: a mean value of pixels in its search window
• Weight: by the patch similarity
y
x
Search Window W
Central pixel x x’s patch area Px
pixel y inside W y’s patch area Py
Assumption: there exists a high degree of redundancy to overcome noise by consulting similar patches to average contributions for a more stable outcome
Post-processing De-noising Filter - NLM
Neighborhood filters – Non-local Means (NLM)
• x,y,z: spatial variables W : search window, P : patch area around each pixel h : parameter to control the smoothness Ga: Gaussian kernel
x
x
Wy Pttytxa
Wyy
Pttytxa
xhpptG
phpptG
p)/)(exp(
)/)(exp(
22
22
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y
x
What to do now…
Information in the input image is not sufficient
Extend the search space beyond the current image• Utilize prior scans of the same patient:
- Z. Kelm, H. Yu & G. Wang, Q. Xu & G. Wang, J. Ma & Z. Liang, W. Xu & K. Mueller
- simple, but limited• Utilize database of different patients - find reference image and incorporate into the de-noising
Reference-based NLM (R-NLM)
Compare between central patch and the reference patch
Input Ref
weight, pixel value
y
x
22
22
exp( ( ) / )
exp( ( ) / )
y t
x
y t
x
crp crpa x t y
y W t Px
crpa x t
y W t P
G t p p h p
pG t p p h
Matched Reference-based NLM (MR-NLM)
Input Matched-R Clean-R
pixel valueweight
22
22
exp( ( ) / )
exp( ( ) / )
y t
x
y t
x
drp crpa x t y
y W t Px
drpa x t
y W t P
G t p p h p
pG t p p h
Refinement to MR-NLM
The refinement to NLM is also applicable to MR-NLM
Implement two redundancy control methods• Reduce search window redundancy [T. Tasdizen]: discard unrelated pixels whose mean and variance are different enough• Reduce patch redundancy [P. Coupe et al.]: apply PCA to high-D patch space project patches to a lower dimensional sub-space
Improve not only efficiency but also accuracy
Online Database Construction
2D Image Space High-D Image Feature Space
Image Scan Global Image Feature
Exact as salient local image structure and contextual information
Learn the cluster centers of the local features of all images and label them
Concatenate local labels to form global descriptor as distinct salient properties of the image
Local Image Feature Descriptor
In MR-NLM:• Input image is low-dose• The database contains only high (normal)-dose images • Matching is between artifact-free and artifact-contained
ones local feature descriptor should be tolerant to artifact (streak, noise, etc.) and small deformation
Scale-Invariant Feature Transform (SIFT) feature• Captures histogram of edge orientations in a local
neighborhood• Scale-invariant, transform-invariant and less sensitive to
noise
Local Image Feature Descriptor
SIFT feature descriptor:• Over the neighborhood of size 1616 dividing to 44 blocks• In each block, 8-orientation histogram of edges is
computed
Dense SIFTs over a regular spaced grid: better, robust• Grid spacing of 8 pixels, N = 3232 (6464) SIFTs for 2562
(5122) image
block
8-bin orientation histogram
neighborhood
448 128-D feature vector
Learn visual words
• To describe one image, the dimension is reduced from 128•N to N (N 1024 or 4096).
A set of local features {S0, S1, .., SN-1}
k-means
clustering
K cluster centers as visual words {V0, V1,
…, VK-1} as visual vocabulary V
Local feature vector is assigned to index of
the closest visual word
Labeling
Global Image Feature Descriptor
• Partition image to multi-resolution to increase the precision• Concatenate histograms of labels from each sub-region.• Totally, 26•K dimensions (K 50 in this paper)
A set of labels in fixed grid
positions
Spatial pyramid based vector quantization
Global Image
Feature
Dimension
2D Image Space High-D Image Feature Space
Scan Image Global Image Feature
128k-D per image
1k-D per image
1.3k-D per image
64k-D
Online Prior Search
2D Image Space High-D Image Feature Space
Target Image M nearest references
Support Kd-tree structure (PKD-tree) for fast labeling process, check our paper for details
Histogram Intersection
Essentially concatenated histograms while not only high-D vector; histogram intersection vs. Euclidean distance
Online De-noising
Registration FBP
De-noised image
MR-NLM
Target image, M nearest references, Low-dose condition
SIFT-flow• Tolerant to noise and
small deformation• Optical-flow to
obtain displacement field
• SIFT instead of pixel
Refined MR-NLM• Two redundancy
controls• Fall back to regular NLM
for pixel with close to zero normalization factor
Experiments
Two image databases (not pre-aligned):• 48 2562 head scans - 15 NIH visible human head images - 33 CT cadaver head images• 150 5122 human lung scans from two patients - “give a scan” online database
Original reconstructions are utilized as:• Basis for low-dose simulation (limited number of
projections with noise)• Basis for generating target scan (deformed or rotated and
then reconstruct with low-dose condition)• Gold standard for evaluation
Fan-beam geometry
Future Works
PCA reduction to global image feature
Larger database for more experiments to verify effectiveness
GPU acceleration