Bayesian Parallel Imaging with Edge-Preserving Priors

Scientist

Ashish Raj

Introduction

Existing parallel imaging methods are limited by a fundamental tradeoff, where suppressing background noise introduces aliasing artifacts. Reconstructed data is further degraded by sensitivity errors due to physiological motion, coil misalignment and insufficient calibration lines. Current regularization techniques either impose minimum norm, or require a prior image mean estimate. The limitations of these regularization techniques are clear: regularized SENSE makes unrealistic assumptions about the image norm, while methods relying on a prior estimate must be carefully registered to the target. Use of such strong reference priors is vulnerable to errors in their estimation, leading to reconstruction artifacts. Tikhonov regularization incorporates spatial information, but unfortunately assume that intensities are globally smooth, leading to excessive blurring of edges. We introduce an edge-preserving prior that instead assumes that intensities are piecewise smooth, and show how to efficiently compute its Bayesian estimate. Our prior model is quite general, and has very few parameters; hence little or no effort is required to find this prior, in contrast to image-based or temporal priors. The estimation task is formulated as an optimization problem, which requires minimizing a non-convex objective function in a space with thousands of dimensions. As a result, traditional continuous minimization methods cannot be applied. However, our optimization problem is closely related to some problems in computer vision for which discrete optimization methods based on graph cuts have been developed in the last few years. We show how to extend these algorithms to address our optimization problem, and call it EPIGRAM (Edge-Preserving Parallel Imaging with Graph Cut Minimization).

Results

Fig 1 shows reconstruction of a central sagittal MPRAGE slice using an 8-channel head coil on a 4T Bruker /Siemens machine, with an undersampling factor R=4. The sum of squares image is shown in (a), regularized SENSE with (empirically obtained optimal) µ = 0.12 in (b), regularized SENSE with µ = 0.24 in (c) and EPIGRAM in (d). Considerable SNR improvement is observed in the EPIGRAM reconstruction, compared to both SENSE reconstructions. Higher regularization in SENSE caused unacceptable residual aliasing, as observed by (c). Fig 2 shows similar results for an axial torso scan; SENSE was regularized with µ = 0.16 in (b) and (e).

Figure 1

Figure 2

Future work will involve extending these algorithms to time-resolved dynamic imaging situations, like perfusion, diffusion and functional imaging, as well as spectroscopic imaging. In each of these cases there exists an additional dimension on which the concept of neighbourhood similarity is well-defined. Therefore extending the Markovian prior to include the additional dimension is likely to drastically enhance the power of the prior.

Publications

1. Raj A, Singh G, Zabih R, Wang Y, Schuff N, Weiner M. Bayesian Parallel Imaging with Edge-Preserving Priors. Magnetic Resonance in Medicine, in print.
2. Raj A, Singh G, Zabih R. MRIs for MRFs: An Extended Graph Cut Algorithm For Generalized Deconvolution Problems in MR and Vision. IEEE Computer Vision and Pattern Recognition Conference 2006; 1061-1069.
3. Raj A. A Signal Processing And Machine Vision Approach to Problems in Magnetic Resonance Imaging. PhD Thesis 2006, Cornell University.
4. Raj A, Zabih R. A Graph Cut Algorithm For Generalized Image Deconvolution. Proc. International Conference of Computer Vision 2005: 1901.
5. Kolmogorov V, Zabih R. What Energy Functions Can Be Minimized Via Graph Cuts? IEEE Transactions on Pattern Analysis and Machine Intelligence 2004; 26(2): 147-59