Shinohara Hiroyuki, Hori Kensuke, Hashimoto Takeyuki
Faculty of Health Sciences, Tokyo Metropolitan University, 7-2-10, Higasi-ogu, Arakawa-ku, Tokyo, 116-8551, Japan.
Department of Radiology, Showa University Fujigaoka Hospital, 1-30, Fujigaoka, Yokohama-shi, 227-8501, Japan.
Ann Nucl Med. 2023 Nov;37(11):596-604. doi: 10.1007/s12149-023-01862-9. Epub 2023 Aug 23.
Non-blinded image deblurring with deep learning was performed on blurred numerical brain images without point spread function (PSF) reconstruction to obtain edge artifacts (EA)-free images. This study uses numerical simulation to investigate the mechanism of EA in PSF reconstruction based on the spatial frequency characteristics of EA-free images.
In 256 × 256 matrix brain images, the signal values of gray matter (GM), white matter, and cerebrospinal fluid were set to 1, 0.25, and 0.05, respectively. We assumed ideal projection data of a two-dimensional (2D) parallel beam with no degradation factors other than detector response blur to precisely grasp EA using the PSF reconstruction algorithm from blurred projection data. The detector response was assumed to be a shift-invariant and one-dimensional (1D) Gaussian function with 2-5 mm full width at half maximum (FWHM). Images without PSF reconstruction (non-PSF), PSF reconstruction without regularization (PSF) and with regularization of relative difference function (PSF-RD) were generated by ordered subset expectation maximization (OSEM). For non-PSF, the image deblurring with a deep image prior (DIP) was applied using a 2D Gaussian function with 2-5 mm FWHM. The 1D object-specific modulation transfer function (1D-OMTF), which is the ratio of 1D amplitude spectrum of the original and reconstructed images, was used as the index of spatial frequency characteristics.
When the detector response was greater than 3 mm FWHM, EA in PSF was observed in GM borders and narrow GM. No remarkable EA was observed in the DIP, and the FWHM estimated from the recovery coefficient for the deblurred image of non-PSF at 5 mm FWHM was reduced to 3 mm or less. PSF of 5 mm FWHM showed higher spatial frequency characteristics than that of DIP up to around 2.2 cycles/cm but was lower than the latter after 3 cycles/cm. PSF-RD showed almost the same spatial frequency characteristics as that of DIP above 3 cycles/cm but was inferior below 3 cycles/cm. PSF-RD has a lower spatial resolution than DIP.
Unlike DIP, PSF lacks high-frequency components around the Nyquist frequency, generating EA. PSF-RD mitigates EA while simultaneously suppressing the signal, diminishing spatial resolution.
在不进行点扩散函数（PSF）重建的情况下，对模糊的数字脑图像进行深度学习非盲图像去模糊处理，以获得无边缘伪影（EA）的图像。本研究利用数值模拟，基于无EA图像的空间频率特性，探讨PSF重建中EA的机制。
在256×256矩阵脑图像中，将灰质（GM）、白质和脑脊液的信号值分别设为1、0.25和0.05。我们假设二维（2D）平行光束的理想投影数据，除探测器响应模糊外无其他退化因素，以便使用从模糊投影数据中重建PSF的算法精确掌握EA。探测器响应假定为半高宽（FWHM）为2 - 5毫米的平移不变一维（1D）高斯函数。通过有序子集期望最大化（OSEM）生成无PSF重建的图像（非PSF）、无正则化的PSF重建图像（PSF）以及相对差异函数正则化的PSF重建图像（PSF - RD）。对于非PSF，使用FWHM为2 - 5毫米的二维高斯函数通过深度图像先验（DIP）进行图像去模糊处理。将一维特定对象调制传递函数（1D - OMTF），即原始图像和重建图像的一维振幅谱之比，用作空间频率特性指标。
当探测器响应的FWHM大于3毫米时，在GM边界和狭窄GM区域观察到PSF中的EA。在DIP中未观察到明显的EA，并且对于非PSF去模糊图像，在5毫米FWHM下从恢复系数估计的FWHM降低到3毫米或更小。5毫米FWHM的PSF在约2.2周期/厘米之前显示出比DIP更高的空间频率特性，但在3周期/厘米之后低于DIP。PSF - RD在3周期/厘米以上显示出与DIP几乎相同的空间频率特性，但在3周期/厘米以下较差。PSF - RD的空间分辨率低于DIP。
与DIP不同，PSF在奈奎斯特频率附近缺乏高频成分，从而产生EA。PSF - RD减轻了EA，同时抑制了信号，降低了空间分辨率。
