Non-Linear Extended Filter with Near Unit-Gain Feedback Loop Yields High Quality, Fast MENT CT Reconstruction

Abstract

<p>High-quality, fast 3D tomographic reconstruction of objects from projections remains challenging, especially in noisy, sparse, and high contrast measurement environments. Current linear and non-linear iterative processing methods are limited in their ability to extract diagnostic information. To improve information extraction, we propose a new object density estimator with near-unity feedback loop gain, called extended High Efficiency CT with Optimized Recursions (eHECTOR). This algorithm converges to the maximum entropy (MENT) voxel estimator with non-linear transformations. An iterated small signal linearized extended filter with near-unit filtered back-projection (FBP) loop gain refines the object density estimate while increasing resolution. This new model requires little code, reduces data manipulation, and improves accuracy and speed of convergence. Every iteration through the non-linear filter provides effective error minimization in all voxel degrees of freedom of the high-dimensional voxel state space. The proposed method overcomes limitations of current state-of-the-art non-linear reconstruction, which is limited to low-dimensional subspace error contraction, thus limiting the rate of convergence in the high-dimensional voxel space. The proposed method provides improved information extraction, numerical stability, and efficient use of computational resources while minimizing numerical errors and noise sensitivity. It has broad clinical and industrial applications due to its efficiency, accuracy, and high speed. It allows for reduced radiation, smaller X-ray spot size, concurrent modeling of movement, and system calibration while reducing noise, image blur, and artifacts.</p>