提出sFRC方法，用傅里叶环相关检测医学图像恢复中的幻觉问题。

Deep learning (DL) methods are currently being explored to restore images from sparse-view-, limited-data-, and undersampled-based acquisitions in medical applications. Although outputs from DL may appear visually appealing based on likability/subjective criteria (such as less noise, smooth features), they may also suffer from hallucinations. This issue is further exacerbated by a lack of easy-to-use techniques and robust metrics for the identification of hallucinations in DL outputs. In this work, we propose performing Fourier Ring Correlation (FRC) analysis over small patches and concomitantly (s)canning across DL outputs and their reference counterparts to detect hallucinations (termed as sFRC). We describe the rationale behind sFRC and provide its mathematical formulation. The parameters essential to sFRC may be set using predefined hallucinated features annotated by subject matter experts or using imaging theory-based hallucination maps. We use sFRC to detect hallucinations for three undersampled medical imaging problems: CT super-resolution, CT sparse view, and MRI subsampled restoration. In the testing phase, we demonstrate sFRC's effectiveness in detecting hallucinated features for the CT problem and sFRC's agreement with imaging theory-based outputs on hallucinated feature maps for the MR problem. Finally, we quantify the hallucination rates of DL methods on in-distribution versus out-of-distribution data and under increasing subsampling rates to characterize the robustness of DL methods. Beyond DL-based methods, sFRC's effectiveness in detecting hallucinations for a conventional regularization-based restoration method and a state-of-the-art unrolled method is also shown.