Citation:
C. Marianno, J. Ellsworth, and W. Sanders “Optimizing the Number of Angles for Reconstructing a 2D Image from a Hardware Radon Transform”, Symposium on Radiation Measurements and Applications (SORMA), 21-24 July 2025, Berkeley, California.
Abstract:
Radiography has been an invaluable tool to access the inner structure of the world around us. The trend is now firmly heading in the direction of adding time to the dimensions that radiography can access. The number and pacing of frames continue to rise as researchers probe the dynamics of evolving configurations and reactions. Multi-frame radiography with a pixelated detector has a fundamental limit of frame pacing with respect to image resolution born out of the serial readout of a column of pixels. With a fixed readout speed, field of view or spatial resolution must be sacrificed to maintain frame pacing. While buffering pixels within the detector can provide a limited amount of independence, the fabrication challenge goes up exponentially as the number of buffered frames rises. As proposed in “Utilizing Parallel Hardware Radon Transforms for Radiographic Imaging” (to be published in Nuclear Instruments and Methods A), this limit can be broken by instead sampling the 2D image in parallel via a simultaneous hardware approximated Radon transform. While the theory is demonstrated to yield viable reconstruction results, the number of angles sampled has a strong impact on the residual error in the reconstructed image. In this research, the relationship between angles and detector pitch is characterized and optimized to determine the greatest return on addition of angles. This approach gives application flexibility to determine if targeting a maximal residual error is more important than maximal performance and informs the balance of individual element efficiency vs. scatter and beam depletion. A dataset of 17 chest radiographs was compiled to sample a diverse range of contrasts, edges, and radiography blur mechanisms with under-sampled to over-sampled transforms and reconstructions. A common model for the root mean squared error (RMSE) performance accommodating continuous pitch and angles values was built which proved robust against numeric artifacts within the reconstruction. RMSE values quickly asymptote at less than 5% full scale and were insensitive to bit depth. Overall the shape of the curve was nominally consistent for any given base image and pitch but the magnitude was correlated to pitch and base image quality. The optimal number of angles was defined as the point the RMSE changed less than 1% compared to the previous angle trial. This model was then validated against the training set as well as other non-related images to validate its generalized performance. Even at full optimization, the required number of angles results in a significant decrease in the number of required elements compared to a fully pixelated sensor. Improving from parity at 1.7 mm spatial pitch to only 49% at 0.5 mm, to 13% the number of elements at 0.1 mm. This reduction in elements combined with the physically larger scale of the elements (printed circuit board vs. integrated circuit architectures) dramatically increases the manufacturability of the imager over in-detector buffered pixelated cameras of comparable speeds with dramatically higher frame counts.