Restoration of MRI data for intensity non-uniformities using local high order intensity statistics - PubMed (original) (raw)

Restoration of MRI data for intensity non-uniformities using local high order intensity statistics

Stathis Hadjidemetriou et al. Med Image Anal. 2009 Feb.

Abstract

MRI at high magnetic fields (>3.0 T) is complicated by strong inhomogeneous radio-frequency fields, sometimes termed the "bias field". These lead to non-biological intensity non-uniformities across the image. They can complicate further image analysis such as registration and tissue segmentation. Existing methods for intensity uniformity restoration have been optimized for 1.5 T, but they are less effective for 3.0 T MRI, and not at all satisfactory for higher fields. Also, many of the existing restoration algorithms require a brain template or use a prior atlas, which can restrict their practicalities. In this study an effective intensity uniformity restoration algorithm has been developed based on non-parametric statistics of high order local intensity co-occurrences. These statistics are restored with a non-stationary Wiener filter. The algorithm also assumes a smooth non-uniformity and is stable. It does not require a prior atlas and is robust to variations in anatomy. In geriatric brain imaging it is robust to variations such as enlarged ventricles and low contrast to noise ratio. The co-occurrence statistics improve robustness to whole head images with pronounced non-uniformities present in high field acquisitions. Its significantly improved performance and lower time requirements have been demonstrated by comparing it to the very commonly used N3 algorithm on BrainWeb MR simulator images as well as on real 4 T human head images.

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Figures

Fig. 1

Fig. 1

Example phantom T1 images from the BrainWeb MR simulator. In the first row in (a) is the true phantom, in the second row is a phantom image without intensity non-uniformity but with high superimposed noise, and in the third row is a phantom with high non-uniformity and some superimposed noise. Next to each image in (b) is its co-occurrence density matrix. In (c) are their corresponding restoration matrices where the gain factors are linearly proportional to the intensities.

Fig. 2

Fig. 2

The shape of the Wiener restoration filter in both the radial r and angular ϕ dimensions.

Fig. 3

Fig. 3

The radial and angular sizes of the non-stationary Wiener restoration filter fq depend on the position of its center point in the co-occurrence matrix.

Fig. 4

Fig. 4

The first row shows a BrainWeb phantom with both high non-uniformity B = 40% and high noise _N_I = 5%. The second row shows the rough estimate of its non-uniformity and in the third row is the smooth estimate of its non-uniformity.

Fig. 5

Fig. 5

A block summary of the algorithm.

Fig. 6

Fig. 6

The error images of the restorations of the BrainWeb MR phantoms corrupted with a non-uniformity of 40% and a noise level of 5% for T1, T2, and PD are in (a), (b), and (c), respectively. The first column shows the original corrupted phantom. In the second column is the true non-uniformity field. The remaining two columns show the error images for the N3 and the co-occurrence restorations, respectively. The dynamic range used for the display of both error images is the same. In all cases the error images resulting from the N3 restorations are brighter which correspond to higher error.

Fig. 7

Fig. 7

Examples of restorations of four of the 4 T human head images given in Table 7. In each example the first row shows the acquired image, the second row shows the correction with N3, and in the third row is the restoration with the co-occurrence algorithm. The N3 restoration contains a considerable residual of the non-uniformity and sometimes it even accentuates the non-uniformity. It also darkens the white matter and introduces overshooting contours around the borders between regions with different intensities such as between the gray matter and the white matter at the cortex. The higher uniformity of the white matter intensity seen in the images corrected with the co-occurrence algorithm is an indication of its improved performance.

Fig. 8

Fig. 8

Radial standard deviation of a tissue distribution due to intensity non-uniformity.

Fig. 9

Fig. 9

The effect of intensity non-uniformity on the angular spread of the co-occurrences and the size of the Wiener restoration filter.

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