Imprecise expectations for imprecise linear filtering

A generalization of the maximum likelihood expectation maximization (MLEM) method: Masked-MLEM

Objective.In our previous work on image reconstruction for single-layer collimatorless scintigraphy, we developed the min-min weighted robust least squares (WRLS) optimization algorithm to address the challenge of reconstructing images when both the system matrix and the projection data are uncertain. Whereas the WRLS algorithm has been successful in two-dimensional (2D) reconstruction, expanding it to three-dimensional (3D) reconstruction is difficult since the WRLS optimization problem is neither smooth nor strongly-convex. To overcome these difficulties and achieve robust image reconstruction in the presence of system uncertainties and projection noise, we propose a generalized iterative method based on the maximum likelihood expectation maximization (MLEM) algorithm, hereinafter referred to as the Masked-MLEM algorithm.Approach.In the Masked-MLEM algorithm, only selected subsets ('masks') from the system matrix and the projection contribute to the image update to satisfy the constraints imposed by the system uncertainties. We validate the Masked-MLEM algorithm and compare it to the standard MLEM algorithm using experimental data obtained from both collimated and uncollimated imaging instruments, including parallel-hole collimated SPECT, 2D collimatorless scintigraphy, and 3D collimatorless tomography. Additionally, we conduct comprehensive Monte Carlo simulations for 3D collimatorless tomography to further validate the effectiveness of the Masked-MLEM algorithm in handling different levels of system uncertainties.Main results.The Masked-MLEM and standard MLEM reconstructions are similar in cases with negligible system uncertainties, whereas the Masked-MLEM algorithm outperforms the standard MLEM algorithm when the system matrix is an approximation. Importantly, the Masked-MLEM algorithm ensures reliable image reconstruction across varying levels of system uncertainties.Significance.With a good choice of system uncertainty and without requiring accurate knowledge of the actual system matrix, the Masked-MLEM algorithm yields more robust image reconstruction than the standard MLEM algorithm, effectively reducing the likelihood of erroneously reconstructing higher activities in regions without radioactive sources.

Non-Additive Imprecise Image Super-Resolution in a Semi-Blind Context

The most effective superresolution methods proposed in the literature require precise knowledge of the so-called point spread function of the imager, while in practice its accurate estimation is nearly impossible. This paper presents a new superresolution method, whose main feature is its ability to account for the scant knowledge of the imager point spread function. This ability is based on representing this imprecise knowledge via a non-additive neighborhood function. The superresolution reconstruction algorithm transfers this imprecise knowledge to output by producing an imprecise (interval-valued) high-resolution image. We propose some experiments illustrating the robustness of the proposed method with respect to the imager point spread function. These experiments also highlight its high performance compared with very competitive earlier approaches. Finally, we show that the imprecision of the high-resolution interval-valued reconstructed image is a reconstruction error marker.