Two-Dimensional Spectral Estimation of Bone X-ray Images with MTF Correction
经MTF修正的骨X射线图象二维谱估计

Determination of degree of osteoporosis from spectrum feature analysis of bone radiographs will provide a screening tool to identify individuals with high fracture risks, and also an objective way to monitor treatment effectiveness reliably. This article shows that since the anisotropic trabecular appear weakly in bone X-ray images and contribute a small portion to the power spectrum, and cause that the signal(trabecular) power spectrum is masked by the noise and the MTF(modulation transfer function) of the imaging system, finding spectral characteristics of trabecular patterns may be considered as an inverse problem. It is assumed that the MTF of the imaging system and the noise introduced by film digitizer are isotropic. The isotropic parts are summarized as the synthetic MTF. An isotropic function have the same projection across all angles. The power spectrum of trabecular patterns can be approximated by reconstructing the 2-D power spectrum from the projection power spectra divided by the synthetic MTF based on Filtered Backprojection Algorithm and Fourier Slice Theorem. Experiments on the bone X-ray images and the synthetic images demonstrate that the anisotropic trabecular pattern have distinguished peaks in the reconstructed power spectrum. Once the signal power spectrum is obtained, it is staightfoward to find maximum peak to estimate the trabecular spacing and the trabecular angle and other texture features to describe the degree of anisotropy. These features are directly related to bone structure, therefore, can be used to produce a summary index to predict the fracture risk.