This document discusses sparse coding super-resolution (ScSR) for single-frame super-resolution of medical images. ScSR uses a sparse representation prior to reconstruct high-resolution images from low-resolution inputs. The document evaluates ScSR on SPECT images with and without additional anatomical information. ScSR improved image quality over bilinear interpolation as measured by higher PSNR scores and recovered finer details in power spectral density analysis. Adding computed tomography, magnetic resonance, or digital phantom data provided negligible further improvement over ScSR alone.

1. Sparse coding Super-Resolution

2. •
–
•
–
•
– Sparse coding Super Resolu1on (ScSR)
•

3. •
–

4. •
•
2
•
( )
Matrix: 768 1024Matrix: 384 512Matrix: 192 256 Matrix: 96 128 Matrix: 48 64

5. •
( )
•

6. - -
•
•
• Nearest neighbor
interpolation
• Bi-linear interpola2on • Bi-cubic interpolation

7. - -
• ( )
( )
•
...
H
L1 L2 Ln
B1
B2
Bn
• Multi-Frame Super-Resolution
H
L
• Single-Frame Super-Resolution

8. Single-frame Super-Resolution
• Single-Frame Super-Resolution
–
( ) ( )
Sparse coding Super-Resolution1): ScSR
–
( )
Sparse Mixing Estimators2): SME
1) Yang, Jianchao, et al. "Image super-resolution via sparse representation."
IEEE transactions on image processing 19.11 (2010): 2861-2873.
2) Mallat, Stéphane, and Guoshen Yu. "Super-resolution with sparse mixing estimators."
IEEE Transactions on Image Processing 19.11 (2010): 2889-2900.

9. •
–

10. - Machine learning -
•
⇒

11. •
–
•
–
•
–

13. •
– Sparse coding Super Resolu1on (ScSR)

14. Sparse coding Super-Resolution
•
•
•

15. •
(eq.1)
(x: X K: x D: K n )
Sparse coding Super-Resolu:on
- -
( )

16. Sparse coding Super-Resolution
- -
•
•
•

17. Sparse coding Super-Resolution
- -
•
– α (Eq.2)
•
• (X0)
(xo: Dh: )
(y: Y F: Dl: λ: )

18. Sparse coding Super-Resolution
- -
• ScSR
(X0)
•
(X*) (eq.4)
(eq.5)
(Xt: t X*: X: Y: S: H: )

19. Sparse coding Super-Resolu2on
- -
• ( )
•

20. •

21. - -
• Sparse coding Super-Resolu2on: ScSR
– SPECT
ScSR
• Sparse Mixing Es2mator: SME
–
SME

22. - -
• Sparse coding Super-Resolu2on: ScSR
– SPECT
ScSR

23. Sparse coding Super-Resolution
- -
•
– + (CT MR NM)
• :
• :
(y: Y F: Dl: λ: )
(Xt: t X: Y: S: H: )

24. •
• + CT †
• + MR †
• + NM (Digital Phantom‡)
† OsiriX DICOM Image Library
‡
CT
MR
Digital
Phantom

25. • SPECT: BrightView X with XCT (Philips)
• Isotope: Tc-99m
• Phantom: Hoffman 3D Brain Phantom
Imaging condition
Collimator Low energy high resolution (LEHR)
Energy Window 140keV 10%
Collection mode continuous
Collection step
(Time)
90step (300sec/rotation)
Rotation number 4rotations 50rotations
Turning radius 15cm
Zoom 1.85
Matrix (Pixel) 128 128
(2.5 2.5mm)
256 256
(1.25 1.25mm)
Reconstruction condition
Method OSEM
Iteration 3
Subset 18
Smoothing filter Butterworth
filter
Cutoff 0.52cycles/cm
Order 8

26. • ScSR
Peak Signal to Noise Ratio (PSNR)
(λ)
(Iteration)
•
Power Spectrum Density (PSD)
Image processing parameter
Lambda 0.0005 0.1000
Iteration 1 10

27. PSNR
• PSNR
• I I’
(mean square error: MSE)
(eq.5) PSNR (eq.6)
…(5)
…(6)

28. •
3)
• 2 (eq.7)
(eq.8)
(eq.9)
p(r): r
v
u
r
Δr
3) CG-ARTS SOCIETY. DIGITAL IMAGE PROCESSING. 2015; 198-200.
PSD
…(7)
…(8)
…(9)

29. Bi-linear interpolation
(256 256)(256 256) (128 128)
- -
ScSR ( + NM)
(256 256)
ScSR ( + MR)
(256 256)
ScSR ( )
(256 256)
ScSR ( + CT)
(256 256)

30. - PSNR ( ) -
• Lambda: 0.0090 Iteration: 3 PSNR (37.6582dB)

31. - PSNR ( + CT) -
• Lambda: 0.0065 Iteration: 3 PSNR (37.6585dB)

32. - PSNR ( + MR) -
• Lambda: 0.0070 Iteration: 3 PSNR (37.6583dB)

33. - PSNR ( + NM) -
• Lambda: 0.0100 Iteration: 3 PSNR (37.6582dB)

34. - PSNR
35.8000
36.0000
36.2000
36.4000
36.6000
36.8000
37.0000
37.2000
37.4000
37.6000
37.8000
Bi-linear interpolation ScSR ( ) ScSR ( + CT) ScSR ( + MR) ScSR ( + NM)
PSNRPSNR [dB]

35. - PSNR
37.6580
37.6581
37.6582
37.6583
37.6584
37.6585
37.6586
Bi-linear interpolation ScSR ( ) ScSR ( + CT) ScSR ( + MR) ScSR ( + NM)
PSNRPSNR [dB]

36. 1.E-16
1.E-15
1.E-14
1.E-13
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
- (PSD) -
:
:
: Bi-linear interpolation
: ScSR ( )
: ScSR ( + CT)
: ScSR ( + MR)
: ScSR ( + NM)
PSD
Spatial Frequency [cycles/pixel]

37. 1.E-16
1.E-15
1.E-14
1.E-13
1.E-12
1.E-11
1.E-10
0.4 0.5 0.6 0.7 0.8 0.9 1
- (PSD) -
PSD
Spatial Frequency [cycles/pixel]
:
:
: Bi-linear interpolation
: ScSR ( )
: ScSR ( + CT)
: ScSR ( + MR)
: ScSR ( + NM)

38. Bi-linear interpolation
(256 256)(256 256) (128 128)
- -
ScSR ( + NM)
(256 256)
ScSR ( + MR)
(256 256)
ScSR ( )
(256 256)
ScSR ( + CT)
(256 256)

39. Bi-linear interpolation
(256 256)(256 256) (128 128)
ScSR ( + NM)
(256 256)
ScSR ( + MR)
(256 256)
ScSR ( )
(256 256)
ScSR ( + CT)
(256 256)
- -

40. Sparse coding Super-Resolution: ScSR
- ( ) -
•
• PSNR
• PSD
– ( )
–

41. Sparse coding Super-Resolution: ScSR
- ( ) -
•
• ScSR
⇒
• :
– SPECT
λ
– Static λ
• :
–
–

42. Bi-linear interpolation
(256 256)(256 256) (128 128)
FBP Hamming filter
ScSR
•
ScSR ( )
(256 256)

43. - -
• Sparse Mixing Estimator: SME
–
SME

44. Bi-linear interpolation (128 128)
(128 128) (64 64)
SME (128 128)

45. 0
20
40
60
80
100
120
EDV ESV
0
5
10
15
20
25
30
35
40
EF
[ml] [%]
: : : Bi-linear interpolation : SME

46. Super-Resolution using Sparse coding
- -
•
–
–
•
– ( )
–