# Presentation: 273407

## Restoration of MRI Data for Intensity Non-uniformities using High Order Neighborhood Statistics

- Stathis Hadjidemetrioua, Colin Studholmeb, Susanne Muellerb, Michael Weinerb, and Norbert Schuffb
- aNCIRE/VA UCSF, San Francisco, CA 94121
- bUCSF, San Francisco, CA 94121

## Problem

- MRI is confounded by non-uniform RF bias field
- More prominent at high fields
- Intensity non-uniformity complicates processing
- Depends on the subject and contrast
- Difficult to predict

*4T T1*

## Current MRI Restoration Methods

- Needs to be robust to subject  and contrast
- Approaches:
- Low pass filtering [Brinkmann et al, 98][Cohen et al,00]-*3T*
- Segmentation [Dawant et al, 93]-*1.5T *[Held et al, 97] -*1.5T *
- Pre-registration to atlas [Leemput et al, 99] -*1.5T *[Pohl et al, 02] -*1.5T *[Studholme et al, 04]-*1.5T *
- Gradient image [Vokurka et al, 99]-*1.5T*[Lai et al, 99]-*1.5 T* [Fan et al, 03]-*1.5 T* [Vovk et al, 04]
- Intensity histogram [Sled et al, 98]-*1.5T*[Likar et al, 01][Ji et al, 07]-*3.0T*
- Assume fields *≤3.0T*, brain extraction, healthy atlas* *

## Image Model

*I**A*, anatomy: Discriminable distributions
*N*, noise: Additive, Gaussian, stationary
*B*, non-uniformity: Multiplicative, smooth
- Locally linear *B** *in* **ρ**=x-x**0*:

- _Image Model_

## Intensity Co-occurrences

- _Intensity Co-occurrences_

- Local intensity coincidences of *u**0** *at *x**0 *with:
- Intensities *u* in annulus *N**x**0* of radius *ρ*
- Order *n* of minimum coincidences* *
- where *h(u, x**0**, **ρ**)** *is histogram
- Parzen window for 2D statistics

| 5 | 10 | 3 | 10 | 3 |
| --- | --- | --- | --- | --- |
| 7 | 6 | 3 | 5 | 2 |
| 8 | 3 | 10 | 7 | 2 |
| 7 | 7 | 3 | 10 | 4 |
| 3 | 7 | 3 | 9 | 7 |

- Image window

- Co-occurrence *C, u**max*x*u**max*

*10*

*3*

- .

*u**0*

*u*

- Center(*x**0*)
- Annulus (Nx0)
- Don’t care

## Co-occurrence of Corrupted Images

*B=0%*
*N=0%*

*B=0%*
*N=5%*

*B=40%*
*N=3%*

*u*

*u**0*

- sharp

- smooth

- elongated

- MNI phantoms

*C*

## Corruption of Co-occurrences by Non-uniformity

- Transform to polar coordinates, *(**r,**Φ**)*
- Radial Gaussian filter, *G(**σ**r**)** *with:
- Angular Gaussian filter, *G(**σ**Φ**)*

*Filter*

*C *of *B=0%*

*C *of *B=40%*

*C *of *B=0%*

*C *of *B=40%*

*r*

*σ**r*

*σ**r* as a function of *r* in *C*

## Standard Deviation of Angular Corruption 

- Angular st. dev. *G(**σ**Φ**)** *:

- _Standard Deviation of Angular Corruption_

*u**0*

*σ**r**a*

*σ**r**b*

*σ**Φ**2*

*r**a*

*r**b*

*u**1*

*σ**r**b*

*σ**r**a*

*σ**Φ**1*

*45**o*

*90**o*

*0**o*

*8**o*

## Restoration Filter for Co-occurrences

- Bounded
- inversion

- Restoration (*R*)-gain* *

- Unmix
*f**q**=G**-1**(**σ**r**)**
*G**-1**(**σ**Φ**)*

- Density* **C** *for *B=40%** *

- Corruption filter

- Weiner restoration filter

## Image Restoration:

- _Image Restoration_:

*Phantom, B=40,N=5*

- Center* x**0*, &
- annulus
*x* *in *N*x**0* index *R:*

*W**rough **(x**0**)*

*W**smooth*

- Gaussian
- Smoothing, *G(**σ**W**)*

## Repeat Restoration Iteratively

- Iterative, *t*
- Preserve* **90%* of intensity range
- End condition for iterations:
- If Shannon entropy of *C* *S(C)* increases, st.dev. of restoration *σ**q* is halved
- Until *σ**q**=1** ** *or *t**maximum*

## Evaluation

- Co-occurrences: *ρ**=9 mm*,* n=3 *
- Whole head processing:
- Non-uniformity over signal region
- Extrapolate to low signal region
- MNI phantom, *T1*, *1.5T*
- Images from elderly population* **T1* *MPRAGE*, *FLAIR*, *4T*
- Comparison with N3 [Sled et al, 98]
- Xeon processor *3.6GHz*, *8 GB of RAM*

## Evaluation with Phantom Images

- Error between true (*B=0*, *N=0*)  and restored:
- Normalize images
- Error value:* **Error=**|**true-restored**|**1*
- Time:
- Cooc.:* **0:27 h*
- N3:* **0:24 h*

## Restoration of Phantom Image

*I**in*
*B=40%*
*N=3%*

*I**restored    *
*N3*

*I**restored*
*Cooccu-rrence*

- Error
- maps

## Evaluation with T1 4T Head Images

- _Evaluation with __*T1*__ __*4T*__ Head Images_

- Entropy ≡ randomness
- Multiple elderly subjects
- Time:
- Cooc:* **1:30 h** *
- N3:* **2:12 h*

## Restoration of Head Image

*I**in**,** **T1,** **4T*

*I**restored    *
*N3*

*I**restored*
*Cooccurrence*

## Restoration of Head Image

*I**in**, T1, 4T*

*I**restored    *
*N3*

*I**restored*
*Co-occurrence*

## Segmentation of White Matter Lesions

- White matter lesions

*I**restored* cooc.

*I**in*

- Subject A                               Subject B

- Restoration of *FLAIR*,* 4T* head images:

## Conclusion

- Features:
- High order co-occurrences favor structured WM/GM
- Stable stopping criterion
- Linear intensity scale
- Robust: Variability in anatomy
- Images of elderly population
- High field (*4T*), whole head images
- Non-uniformity with non-Gaussian statistics
- Sensitive: Regions of similar statistics that are spatially close
- Extensions:
- Images of other MR acquisition types
- Compare with other restoration algorithms