Department of Radiology, Perelman School of Medicine at the University of Pennsylvania, Philadelphia, Pennsylvania 19104-4206.
Med Phys. 2013 Nov;40(11):111912. doi: 10.1118/1.4819942.
In tomosynthesis, super-resolution has been demonstrated using reconstruction planes parallel to the detector. Super-resolution allows for subpixel resolution relative to the detector. The purpose of this work is to develop an analytical model that generalizes super-resolution to oblique reconstruction planes.
In a digital tomosynthesis system, a sinusoidal test object is modeled along oblique angles (i.e., "pitches") relative to the plane of the detector in a 3D divergent-beam acquisition geometry. To investigate the potential for super-resolution, the input frequency is specified to be greater than the alias frequency of the detector. Reconstructions are evaluated in an oblique plane along the extent of the object using simple backprojection (SBP) and filtered backprojection (FBP). By comparing the amplitude of the reconstruction against the attenuation coefficient of the object at various frequencies, the modulation transfer function (MTF) is calculated to determine whether modulation is within detectable limits for super-resolution. For experimental validation of super-resolution, a goniometry stand was used to orient a bar pattern phantom along various pitches relative to the breast support in a commercial digital breast tomosynthesis system.
Using theoretical modeling, it is shown that a single projection image cannot resolve a sine input whose frequency exceeds the detector alias frequency. The high frequency input is correctly visualized in SBP or FBP reconstruction using a slice along the pitch of the object. The Fourier transform of this reconstructed slice is maximized at the input frequency as proof that the object is resolved. Consistent with the theoretical results, experimental images of a bar pattern phantom showed super-resolution in oblique reconstructions. At various pitches, the highest frequency with detectable modulation was determined by visual inspection of the bar patterns. The dependency of the highest detectable frequency on pitch followed the same trend as the analytical model. It was demonstrated that super-resolution is not achievable if the pitch of the object approaches 90°, corresponding to the case in which the test frequency is perpendicular to the breast support. Only low frequency objects are detectable at pitches close to 90°.
This work provides a platform for investigating super-resolution in oblique reconstructions for tomosynthesis. In breast imaging, this study should have applications in visualizing microcalcifications and other subtle signs of cancer.
在断层合成中，已经证明可以使用与探测器平行的重建平面实现超分辨率。超分辨率允许相对于探测器进行亚像素分辨率。本工作的目的是开发一种分析模型，将超分辨率推广到倾斜的重建平面。
在数字断层合成系统中，沿与探测器平面成倾斜角（即“倾斜角”）的正弦测试物体在 3D 发散光束采集几何形状中建模。为了研究超分辨率的潜力，指定输入频率大于探测器的别名频率。使用简单反向投影（SBP）和滤波反向投影（FBP）在物体的范围内沿倾斜平面评估重建。通过比较重建的幅度与物体在不同频率下的衰减系数，计算调制传递函数（MTF）以确定调制是否在超分辨率的可检测范围内。为了实验验证超分辨率，使用测角台将条形图案体模相对于商业数字乳腺断层合成系统中的乳房支撑物沿各种倾斜角定向。
通过理论建模表明，单个投影图像无法解析频率超过探测器别名频率的正弦输入。在 SBP 或 FBP 重建中，沿物体倾斜方向的切片可以正确显示高频输入。此重建切片的傅里叶变换在输入频率处最大化，证明物体已被解析。与理论结果一致，条形图案体模的实验图像显示在倾斜重建中有超分辨率。在各种倾斜角下，通过条形图案的目视检查确定可检测调制的最高频率。最高可检测频率随倾斜角的依赖性与分析模型的趋势一致。如果物体的倾斜角接近 90°，即测试频率垂直于乳房支撑物，那么超分辨率是无法实现的。在倾斜角接近 90°的情况下，只能检测到低频物体。
这项工作为断层合成中倾斜重建中的超分辨率研究提供了一个平台。在乳房成像中，本研究应该在可视化微钙化和其他癌症细微迹象方面有应用。
