Background and objective

Total Variation (TV) minimization algorithms have achieved great attention due to the virtue of decreasing noise while preserving edges. The purpose of this work is to implement and evaluate two TV minimization methods in 3D. Their performance is analyzed through 3D visualization of digital breast tomosynthesis (DBT) data with volume rendering.

Methods

Both filters were studied with real phantom and one clinical DBT data. One algorithm was applied sequentially to all slices and the other was applied to the entire volume at once. The suitable Lagrange multiplier used in each filter equation was studied to reach the minimum 3D TV and the maximum contrast-to-noise ratio (CNR). Imaging blur was measured at 0° and 90° using two disks with different diameters (0.5 mm and 5.0 mm) and equal thickness. The quality of unfiltered and filtered data was analyzed with volume rendering at 0° and 90°.

Results

For phantom data, with the sequential filter, a decrease of 25% in 3D TV value and an increase of 19% and 30% in CNR at 0° and 90°, respectively, were observed. When the filter is applied directly in 3D, TV value was reduced by 35% and an increase of 36% was achieved both for CNR at 0° and 90°. For the smaller disk, variations of 0% in width at half maximum (FWHM) at 0° and a decrease of about 2.5% for FWHM at 90° were observed for both filters. For the larger disk, there was a 2.5% increase in FWHM at 0° for both filters and a decrease of 6.28% and 1.69% in FWHM at 90° with the sequential filter and the 3D filter, respectively. When applied to clinical data, the performance of each filter was consistent with that obtained with the phantom.

Conclusions

Data analysis confirmed the relevance of these methods in improving quality of DBT images. Additionally, this type of 3D visualization showed that it may play an important complementary role in DBT imaging. It allows to visualize all DBT data at once and to analyze properly filters applied to all the three dimensions.

Concise Abstract

Total Variation (TV) minimization algorithms are one compressed sensing technique that has achieved great attention due to the virtue of decrease noise while preserve edges transitions. The purpose of this work is to solve the same TV minimization problem in DBT data, by studying two 3D filters. The obtained results were analyzed at 0° and 90° with a 3D visualization through volume rendering. The filters differ in their application. One considers a slice-by-slice optimization, sequentially traversing all slices of the data. The other considers the intensity values of adjacent slices to make this optimization on each voxel. The performance of each filter was also tested with a clinical case. The results obtained were very encouraging with a significantly increased contrast to noise ratio at 0° and 90° and a small reduction in blur at 90° (slight reduction of the out-of-plane artifact).

中文翻译：

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将总变化最小化对乳房断层合成数据的体积渲染可视化的影响。

背景和目标

总变化量（TV）最小化算法由于在保留边缘的同时降低了噪声而获得了极大的关注。这项工作的目的是在3D中实现和评估两种电视最小化方法。通过3D可视化数字乳房断层合成（DBT）数据并进行体积渲染来分析其性能。

方法

两种过滤器均使用真实幻像和一项临床DBT数据进行了研究。一种算法依次应用于所有切片，另一种算法一次性应用于整个体积。研究了每个滤波器方程式中使用的合适的拉格朗日乘数，以达到最小的3D TV和最大的对比度-噪声比（CNR）。使用两个具有不同直径（0.5毫米和5.0毫米）和相同厚度的光盘在0°和90°下测量成像模糊。使用0°和90°的体积渲染分析未过滤和已过滤数据的质量。

结果

对于幻像数据，使用顺序滤波器时，在0°和90°时，分别观察到3D TV值降低25％和CNR分别提高19％和30％。当直接以3D方式应用滤镜时，TV值降低了35％，而CNR在0°和90°时均实现了36％的增长。对于较小的磁盘，两个滤镜在0°时的半峰宽（FWHM）变化为0％，在90°时的FWHM下降了约2.5％。对于较大的磁盘，两个滤波器在0°下的FWHM分别增加2.5％，而在90°下使用顺序滤波器和3D滤波器的FWHM分别降低6.28％和1.69％。当应用于临床数据时，每个过滤器的性能与通过幻象获得的性能是一致的。

结论

数据分析证实了这些方法对提高DBT图像质量的重要性。此外，这种类型的3D可视化显示它可能在DBT成像中起重要的补充作用。它可以一次可视化所有DBT数据，并可以正确分析应用于所有三个维度的过滤器。

简洁摘要

总变化量（TV）最小化算法是一种压缩的传感技术，由于其在保持边缘过渡的同时降低了噪声，因此备受关注。这项工作的目的是通过研究两个3D滤波器来解决DBT数据中相同的电视最小化问题。通过体积渲染通过3D可视化在0°和90°下分析获得的结果。过滤器的应用不同。人们考虑了逐片优化，顺序遍历数据的所有片。另一个考虑相邻切片的强度值以对每个体素进行此优化。每个过滤器的性能也通过临床案例进行了测试。