Blind Deblurring of Spiral CT Images Ming Jiang* School of Mathematics Peking University Beijing 100871, China. Ge Wang Department of Radiology University of Iowa Iowa City, IA 52242, USA Margaret W. Skinner Department of Otolaryngology Washington University Saint Louis, M O 63110, USA Jay T. Rubinstein Department of Otolaryngology University of Iowa Iowa City, IA 52242, USA Michael W. Vannier Department of Radiology University of Iowa Iowa City, IA 52242, USA November 2, 2001 Abstract The temporal bone is a complex paired set of struc- tures at the skull base which contains the organ of hear- ing among others [1]. Treatment of severe to profound, bilateral hearing loss often employs a multi-electrode cochlear implant inserted into the inner ear part of the temporal bone. CT scanners cannot resolve many im- portant temporal bone details, especially bony anatomy. We improve the high-contrast spatial resolution of CT with blind deblurring of CT slices and tested the im- provement using a phantom test object. The improve- ment in visible detail or clinic scans is apparent sub- jectively and approaches 33~ quantitatively. 1 Introduction Spiral/helical computed tomography (CT) is advan- tageous in visualizing and measuring bony structures. However, CT scanners cannot resolve many important temporal bone details, especially those millimeter or sub-millimeter sized structures of the middle and inner ear. In this paper, we developed a blind deblurring al- gorithm to improve the high-contrast spatial resolution of CT sections. Spiral CT can be modeled as a spatially invariant linear system with a 3D Gaussian point spread function (PSF) that is separable and nearly isotropic [2]. As a result, an arbitrary oblique cross-section in an image volume can then be approximated as the convolution g(x) = p(x) ® )~(x), (1) *Currently, Ming Jiang is a visiting professor with Micro-CT Laboratory, Department of Radiology, University of Iowa, Iowa City, IA 52242, USA. where p(x) = a~(x) is the 2-D Gaussian function with standard deviation a, g(x) is the chosen oblique sec- tion, also referred to as the blurred image, and A(x) is the actual cross-section, i.e., the real image. An esti- mate of the real image is called a restored or deblurred image. If the parameter a was known, the EM deblurring algorithm [3] was used to find the deblurred image in [2]. The EM algorithm is well established and has been successfully used in many different applications. For the imaging model (1), the EM algorithm iterates as follows: where/5(x) = p(-x) and ,~k is the deblurred image at iteration k. If the standard deviation a is unknown, that is our case for an arbitrary oblique cross-section, a blind de- blurring/deconvolution algorithm can be used to find the deblurred image and improve image resolution. Blind deblurring can restore a blurred image without prior determination of the PSF. Essentially, we need a good estimate of the standard deviation a. Blind deblurring was recently reviewed [4, 5]. How- ever, all the blind deblurring methods reviewed in [4, 5] require that the PSF and the original image must be irreducible. An irreducible signal cannot be exactly ex- pressed as the convolution of two or more component signals of the same family. However, this fundamental assumption is invalid for the Gaussian PSF. Existing algorithms for Gaussian blind deblurring are not very successful. One popular method is the double iteration scheme developed by Holmes et al. 0-7803-7147-X/01/$10.00@2001 IEEE 1692