Noise Reduction and Brain Tissue Classi cation in MR Images Arvid Lundervold1 and Fred Godtliebsen2
1Norwegian Computing Center, P.O. Box 114, Blindern, N-0314 Oslo, Norway. (E-mail:
[email protected]) 2 Division of Mathematical Sciences, The Norwegian Institute of Technology, N-7034 Trondheim, Norway.
Abstract | The multiparameter dependence of the MR images gives rise to high variability in soft tissue contrast and makes possible in vivo tissue classi cation using multidimensional statistical analysis. Pattern recognition techniques can be used to construct decision rules which enable tissue voxels to be identi ed on the basis of their measurements (i.e. n-tuples of gray level values) in the multispectral MR images. However, noise in the acquisition will a ect the validity and precision of this tissue classi cation. In this study, we investigated the e ect of Gaussian noise and noise reduction techniques upon subsequent tissue classi cation. For image restoration, we employed a non-linear Gaussian window lter before classifying the multispectral MR acquisitions from the head. The Bayesian classi er was based on Haslett's contextual method. In this model, we assumed multinormal class-conditional probability densities, where estimates of the mean vector and covariance matrix for each tissue were obtained from the training data of 14646 labeled pattern vectors which represented 18 di erent types of normal or pathological tissue from a total of 10 patients. The classi cation experiments demonstrated that it was possible to recognize normal brain tissue types and some pathological lesions. Preprocessing with the Gaussian window lter did not improve the tissue classi cation results in the case of images with \normal" noise level. The robustness of the classi er against noise (which is shown to be Gaussian), was explored by adding i.i.d. N (0; i 2 ) noise to each of the channel images, i = 1; : : : ; 4, thus mimicking a \bad day" of the MR instrument. Noisy input severely a ected the classi cation results. However, the number of misclassi cations was clearly reduced after applying a Gaussian window lter with a xed smoothing parameter. Evaluation was done by visual inspection using knowledge of brain anatomy and by computing simple descriptive statistics, residual images, and confusion matrices.
I. MRI data and Training Procedure Multispectral acquisitions of the head from a total of 10 patients were used in the training. All the MR images were acquired at the MR-center in Trondheim, Norway with a 1:5 T Philips Gyroscan system. We used the axial sections with a slice thickness of 6:5 mm, interslice spacing of 6 mm, and the spin-echo (SE) pulse sequence with the following four pulse timing parameter (TR/TE) combinations (i.e. 4 channels) - xed for all examinations: proton density (SE 2200/25), T2 (SE 2200/100), T1 (SE 460/20) pre GdDTPA contrast, and T1 (SE 460/20) post Gd-DTPA contrast. Each channel image was a 256 256 pixel matrix with 12 bit pixel intensity quantization. Field of view was 23 cm (0:9 mm pixel size). All algorithms were coded in C and we employed a SUN Sparc-2 to run the experiments.
A. Image calibration
To obtain a classi er that was transferable between di erent MRI examinations and based on a training set accumulated from several patients, we employed essentially the same calibration procedure as in [8]. The calibration was simply a uniform scaling of the gray level in each channel image so that the mean intensity of white matter, , i = 1; 2; 3; 4 within a selected region of corona radiata obtained a standardized value, 1778, 635, 1402, and 1267, respectively. The calibration procedure could thus be regarded as part of the feature extraction to be performed in both training and test. i
(WM)
B. Training procedure
All supervised labeling of pixels was performed by one of the authors (A.L.). From each patient in the training set we had access to hardcopy images in which regions of interest and diagnosis were speci cally marked by a radiologist. However, for obvious reasons, no precise correspondence between the scanned brain voxels and histopathology could be obtained. Class no. Class name(s), c # pixels, Nc 1-4 air1709 , ... 4109 5-6 arachnoid1711 , ... 505 7-8,39-40 edema 15606 , ... 1179 137 9 carcinoma 40210 1558 10-16 connective tissue 101810 , ... 17-21 CSF1709 , ... 1056 22 dura1810 305 23 fat1707 168 24 glioma 01111 114 638 25-28 gray nuclear1709 , ... 29 infarction5603 37 30 meningioma3607 309 31-32 MS lesion 25012 , ... 97 683 33-35 temporalis muscle1807 , ... 36 white matter17 18 34 35 3149 208 37-38 vascular component 184807 , ... 41 astrocytoma 275606 219 42 porencephaly3607 157 Total: 18 di erent tissue classes, N = 14646 pattern vectors
Table 1: Normal and pathological tissue classes. Subscripts
refer to patient number, subsubscripts denote the slice from where the training pixels were obtained. The numbers following the class names denote the k-means cluster number within which the training pixels were selected (k = 30 or k = 40).
Training was a combination of unsupervised, k-means clustering [6] (k = 30 or k = 40) and supervised pixel labeling within the resulting clusters (cfr. upper part of Figure 1). In the training procedure we labeled 14646 pattern vectors (i.e. pixels) from altogether K = 42 classes (Table 1), representing 18 di erent tissues. After plotting the sample marginal distribution of each class in measurement space, f0; : : : ; 4095g4, it was reasonable to assume multinormal class-conditional densities. Bayes classi cation, employing these multinormaldensities N4 ( ; ) for each class c 2 f1; : : :; K g is illustrated in lower part of Figure 1. c
c
1 2 3 4 16 17 18 19 20 21 24 25 26 27 28 29 31 32 36
air air air air connect CSF CSF CSF CSF CSF glioma gray gray gray gray infarct MS MS white cont.
24 25 26 27 28 29 31 32 36
glioma gray gray gray gray infarct MS MS white
1
2
0.0 1.3 3.2 0.9 18. 52. 51. 45. 53. 48. 46. 56. 60. 47. 30. 57. 68. 70. 35. 21 13. 13. 12. 11. 12. 12. 12. 10. 12.
0.0 2.9 0.6 19. 55. 54. 49. 56. 53. 49. 63. 69. 51. 32. 65. 83. 88. 38. 24 0.0 9.7 8.5 9.1 13. 3.5 6.4 8.9 11.
3
4
16
17
18
19
20
0.0 2.8 19. 50. 45. 46. 44. 46. 49. 62. 71. 51. 31. 67. 81. 92. 39. 25
0.0 18. 54. 53. 48. 55. 51. 48. 61. 67. 50. 32. 63. 78. 82. 37. 26
0.0 16. 23. 21. 20. 16. 9.4 8.7 9.2 9.0 8.9 9.6 9.8 13. 8.8 27
0.0 2.9 7.4 6.1 8.0 13. 21. 19. 18. 21. 13. 15. 19. 21. 28
0.0 4.8 3.6 6.2 17. 28. 24. 23. 24. 14. 16. 18. 21. 29
0.0 2.1 3.2 21. 24. 25. 21. 19. 22. 24. 26. 23. 31
0.0 3.6 16. 24. 22. 20. 22. 16. 18. 21. 21. 32
0.0 2.2 2.6 6.2 8.6 10. 9.3 7.5
0.0 2.6 7.4 8.4 10. 8.2 7.1
0.0 5.4 7.4 8.7 6.9 5.5
0.0 11. 13. 11. 5.7
0.0 4.4 5.9 7.7
0.0 6.1 9.0
0.0 7.4
Table 2: Generalized Mahalanobis distances between all pairs of tissues from a subset of 19 classes in the training set.
II. Pixel classification For all the classi cation experiments we used the Bayes decision rule [1] with minimum expected cost of misclassi cation, and Haslett's contextual model with rst-order neighborhood [4]. An outlier option and a doubt option were not utilized in these experiments. We chose the 0 ? 1 loss function. The prior probabilities of all tissue classes were set equal, = Pr(C = c) = 1=K , c 2 f1; : : :; K g. Figure 1: Training (upper part) and parametric classi cation The contextual part of the Haslett model speci es a set of transition probabilities, j = Pr(C = k j C = l : pixel i P Based on the estimated mean vector, ^ = 1c =1c x ( ) and j are rst-order neighbors). Again, we made a simple P and the sample covariance matrix, ^ = c1?1 =1c (x ( ) ? choice by letting j = 0:9 and j = 0:1=(K ? 1) if l 6= k, ^ )(x ( ) ? ^ ) , where x ( ) = (x 1; : : : ; x 4)( ) 2 R4 de- k; l 2 f1; : : : ; K g. note the transpose of a calibrated pattern vector from class c, we calculated the generalized Mahalanobis distance meaIII. Image Enhancement sure [5], ! = ( 2 + 2)1 2 between all pairs k; l of tissue classes. Here, 2 = ( ? ) ?1 ( ? ), To perform noise reduction we employed the non-linear
2 = 4log jk j =jjjl j = , and = 21 ( + ). This disGaussian window lter as this has been shown in MRI to tance measure was used to estimate the separability or the be superior to other methods [2, 3]. amount of overlap of the multivariate distributions for evLet g denote the observed grey value at pixel b, and let ery pair of tissue classes in pattern space, R4 (Table 2). It D denote a window centered at pixel b. We employed a is shown by Hjort [5] that for the pairwise error rate , square 3 3 window. The Gaussian window lter estimates the relation ^ =: (? 12 !^ ) holds as a reasonable ap- the true value f at pixel b by proximation. A generalized Mahalanobis distances greater than 4:0 will thus give a tentative pairwise error rate less X 1 e? ( i ? b) g ; v = X e? ( i? b ) (1) than 2:5%, assuming multinormal class-conditional densi- f^ = ties. 2 b 2 bv c
N
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1 2
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Here, is a smoothing parameter to be adjusted in the occur frequently within air having a low signal intensity. Lower particular application or estimated from the data when right: Same as lower left, but after Gaussian 3 3 window ltering the noise standard deviation, is known. Since the with = 261:6 ( = 95:7, = 57:5). estimation procedure is very time consuming we selected = 2 throughout this study, However, this is in accordance with estimation of in other MR acquisitions using the same MR instrument [3]. noise
noise
noise
noise
IV. Experimental Results In the test phase of a closely related study [7], based on the same set of 14646 training pixels, 106 images from 15 other patients were classi ed (without noise ltering) using Haslett's contextual method. Here, we found that normal tissue to a large extent were correctly classi ed. However, there was considerable variation between the patients with respect to the quality of pathological tissue recognition, often with unacceptable or low speci city. The e ect of Gaussian window ltering, both in the original acquisitions and after the addition of i.i.d. Gaussian noise, is illustrated in Figure 2. The noise suppression is visually evident and seems not to remove anatomical detail nor introduce spurious new ones. Results from the following contextual classi cation are depicted in Figure 3. Figure 3: The e ect of noise and noise reduction on contextual classi cation using Haslett's method. (Same acquisitions
and layout as in Fig. 2) Interpretation of gray levels: air & compact bone 7! white (250); CSF 7! dark gray (86); gray matter 7! medium gray (150); white matter 7! light gray (200); all other classes 7! black (0). Unclassi ed pixels 7! very light gray (230).
References
Figure 2: Noisy and Gaussian window ltered MR images.
(White matter calibrated channel 1 (SE 2200/25) from patient 18 with normal MRI ndings.) All noise calculations were performed within a mask (7857 pixels) surrounding the head covering air only. The depicted detail is a 128 128 subimage of the frontal part of the brain. Upper left: Un ltered image (noise = 49:0, noise = 26:8). Upper right: Same as upper left, but after Gaussian 3 3 window ltering with = 53:6 (noise = 47:9, noise = 12:7). Lower left: Same as upper left, but after i.i.d. N (0; 132) noise addition (noise = 103:8, noise = 130:8). The increase in noise after adding noise is due to the censoring e ect at gray level 0 which happens to
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