MR. TOMP : Inversion of the Modulo Radon Transform (MRT) via Orthogonal Matching Pursuit (OMP)
MR. TOMP : Inversion of the Modulo Radon Transform (MRT) via Orthogonal Matching Pursuit (OMP)
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DOI：
10.1109/icip46576.2022.9897428
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Matthias Beckmann;Ayush Bhandari
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文献类型：
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作者：
Matthias Beckmann;Ayush Bhandari
近年来，断层摄影领域的从业者提出了高动态范围（HDR）解决方案，其灵感来自计算摄影中的多曝光融合策略。为此，在不同的曝光下采集多个拉冬变换投影，这些投影在算法上被融合以促进HDR重建。在我们最近的工作中，提出了一种基于模拉东变换（MRT）的单次曝光替代多曝光融合方法。在这种情况下，Radon变换投影通过模非线性进行折叠。该折叠允许HDR值被映射到传感器的动态范围中，并且因此避免饱和或削波。然后使用算法将折叠的测量值映射回其环境范围。本文的主要目标是介绍一种新颖的傅里叶域恢复方法，即OMP-FBP方法，该方法基于正交匹配追踪（OMP）算法和滤波反投影（FBP）公式。所提出的OMP-FBP方法提供了几个优点，它是不可知的模阈值或折叠的数量，可以处理比以前的方法低得多的采样率，是经验稳定的噪声和离群值。本文通过计算机仿真和硬件实验验证了OMP-FBP恢复方法的有效性。
In the recent years, practitioners in the area of tomography have proposed high dynamic range (HDR) solutions that are inspired by the multi-exposure fusion strategy in computational photography. To this end, multiple Radon Transform projections are acquired at different exposures that are algorithmically fused to facilitate HDR re-construction. A single-shot alternative to multi-exposure fusion approach has been proposed in our recent line of work which is based on the Modulo Radon Transform (MRT). In this case, Radon Transform projections are folded via modulo non-linearity. This folding allows HDR values to be mapped into the dynamic range of the sensor and, thus, avoids saturation or clipping. The folded measurements are then mapped back to their ambient range using algorithms. The main goal of this paper is to introduce a novel, Fourier domain recovery method, namely, the OMP-FBP method, which is based on the Orthogonal Matching Pursuit (OMP) algorithm and Filtered Back Projection (FBP) formula. The proposed OMP-FBP method offers several advantages; it is agnostic to the modulo threshold or the number of folds, can handle much lower sampling rates than previous approaches and is empirically stable to noise and outliers. Computer simulations as well as hardware experiments in the paper validate the effectivity of the OMP-FBP recovery method.