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Motion artifacts are a significant issue in medical image reconstruction. There are many methods for incorporating motioninformation into image reconstruction. However, there are fewer studies that focus on deformation regularization in motioncompensatedimage reconstruction. The usual choice for deformation regularization has been penalty functions based onthe assumption that tissues are elastic. In the image registration field, there have been some methods proposed that imposedeformation invertibility using constraints or regularization, assuming that organ motions are invertible transformations.However, most of these methods require very high memory or computation complexity, making them poorly suited fordealing with multiple images simultaneously in motion-compensated image reconstruction. Recently we proposed animage registration method that uses a simple penalty function based on a sufficient condition for the local invertibility ofdeformations.1 That approach encourages local invertibility in a fast and memory-efficient way. This paper investigatesthe use of that regularization method for the more challenging problem of joint image reconstruction and nonrigid motionestimation. A 2D PET simulation (based on realistic motion from real patient CT data) demonstrates the benefits of suchmotion regularization for joint image reconstruction/registration

Joint image reconstruction and nonrigid motion estimation with a simple penalty that encourages local invertibility