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Non-Linear Extended Filter with Near Unit-Gain Feedback Loop Yields High Quality, Fast Maximum Entropy CT Reconstruction
  • Wolfram Jarisch
Wolfram Jarisch
Cyber Technology, Cyber Technology

Corresponding Author:[email protected]

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Abstract

We’re pioneering a novel method in interventional CT radiography, designed to streamline the process of CT down to utilizing a mere six projections. Nonetheless, a phenomenon akin to unfiltered backprojection’s object blurring was noted as the number of projections increased. This observation prompted us to explore the efficacy of high-pass projection data filtering, an element intrinsic to filtered backprojection (FBP) type reconstruction. We successfully computed the Maximum Entropy (MENT) estimate in an efficient manner by integrating the definition for MENT (Cover & Thomas; 2006) with non-linear filtering, comparable to the extended Kalman filter (Dan Simon; 2006). This reformulated approach replaces the formerly used multiplicative operations with logarithmic and exponential data transformations.
To accelerate the reconstruction process, we implemented progressive resolutions. This involves initially preparing smaller-sized (condensed) projections to a scale of single pixels and commencing with a singular voxel for the initial reconstruction iterations. In producing these condensed projections, we maintained the white projection measurement noise. Consequently, as the reconstruction escalates in resolution, the main source of estimation noise originates from the high(er)-resolution projections.
The efficacy of our methodology was validated in both parallel and cone-beam reconstruction, thereby inciting an in-depth analysis of the estimation process. The iterative cycle, which incorporates projection, backprojection, and intermediate non-linear data transformations, mirrors the data flow within a nonlinear extended Kalman filter (eKF), suggesting the comparable strategy. Our new approach has a wide range of applications and is capable of encompassing all FBP-type algorithms. Within the filter model we utilized the progressive resolution recursively, beginning with the selected projection resolution, followed by a state estimate in the extended filter, and finally the MENT object density estimate. A loop gain marginally below unity, sustained even during the final iterations, still assists effectively in compensating minimal residual projection measurement errors.