利用HOTV正则化从低分辨率电子断层扫描数据中恢复细节
Recovering Fine Details from Under-Resolved Electron Tomography Data using HOTV Regularization
AI总结：
本文提出基于高阶总变分（HOTV）的正则化方法，用于改进电子断层扫描中细节恢复，尤其在处理实际采样模式和精细图像特征时表现更优。
摘要：
在过去十年中，使用ℓ₁正则化（通常归类为压缩感知算法）的重建方法显著提升了电子断层扫描高保真成像能力。电子断层扫描中最流行的ℓ₁正则化方法是总变分（TV）正则化。除了减少噪声外，TV正则化鼓励分段常数解，具有稀疏边界区域。本文提出了一种基于高阶总变分（HOTV）的替代ℓ₁正则化方法用于电子断层扫描。与TV类似，HOTV方法促进具有稀疏边界区域的解。然而，在平滑区域中，解不限于分段常数行为。我们证明这种特性允许更准确地重建更广泛的图像类别——即使对于TV最初设计的图像也不例外，特别是在处理实际断层扫描采样模式和非常精细的图像特征时。我们为电子断层扫描数据集和一个幻影示例开发了结果，并与其他离散断层扫描方法进行了比较。
英文摘要：
Over the last decade or so, reconstruction methods using $\ell_1$ regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular $\ell_1$ regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative $\ell_1$ regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images -- even those for which TV was designed for -- particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. We develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.
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