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Medical Image Interpolation—The Quest for Higher Quality

M. Unser

Plenary talk, Proceedings of the 2004 IEEE Nuclear Science Symposium, Medical Imaging Conference, Fourteenth International Workshop on Room-Temperature Semiconductor x- and Gamma- Ray Detectors, Special Focus Workshop (Sensing, Control and Readout of Gravitational Wave Detectors), Special Focus Workshop (Synchrotron Radiation Detectors), 2004 Workshop on the Nuclear Radiology of Breast Cancer (NSS/MIC/RTSD'04), Roma, Italian Republic, October 16-22, 2004, pp. 130.



Interpolation plays a crucial role in medical image processing. It is required for tomographic reconstruction (filtered backprojection, inverse Fourier or iterative reconstruction), for medical image visualization (in 2D or 3D), for image registration (rigid-body or elastic matching), and feature extraction (contours, differential geometry). In this presentation, we give an overview of recent developments in image interpolation, with an emphasis on spline-based methods that have been found to provide the best tradeoff between image quality and computational cost. To this end, we consider a generalized interpolation model where images are represented as weighted sums of compactly supported basis functions (e.g., B-splines)—not necessarily interpolating—that are positioned on a regular grid at the pixel (or voxel) locations. The expansion coefficients are determined by fitting the model to the image data; this leads to an efficient interpolation algorithm based on recursive digital filtering. We present a quantitative Fourier analysis that allows the objective comparison of interpolators associated with different basis functions. We show that a key determinant of reconstruction quality is the order of approximation of the representation. In this respect, polynomial B-splines have the remarkable property of having the minimal support for a given order of approximation, which explains their superior performance. We present some experimental comparisons of interpolators that perfectly correlate with the theoretical predictions. The advantage of high-quality interpolation is illustrated with a rigid-body registration task where it has a dramatic effect on accuracy at the subpixel level.

The final part of the talk is devoted to the problem of interpolation in the presence of noise. We show that this can be achieved analogously, using the same type of representation and filtering algorithm, by means of a so-called smoothing spline. The key is to introduce some a priori knowledge on the type of signal (in the form of a regularization functional or a covariance function) and on the statistical distribution of the noise. We present several formulations of the problem—variational (Tikhonov), MMSE estimator (Wiener), and Bayesian—which lead to equivalent solutions (optimum function space plus corresponding filtering algorithm) under the Gaussian hypothesis.

Slides of the presentation (PDF, 2.8 Mb)


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