Weighted singular value decomposition (wSVD) to improve the radiation dose efficiency of grating based x-ray phase contrast imaging with a photon counting detector

The noise performance of grating-based differential phase contrast (DPC) imaging system is strongly dependent on the fringe visibility of the grating interferometer. Since the grating interferometer system is usually designed to be operated at a specific energy, deviation from that energy may lead to visibility loss and increased noise. By incorporating an energy-discriminating photon counting detector (PCD) into the system, photons with energies close to the operation energy of the interferometer can be selected, which offers the possibility of contrast-to-noise ratio (CNR) improvement. In our previous work, a singular value decomposition (SVD)-based rank one approximation method was developed to improve the CNR of DPC imaging. However, as the noise level and energy sensitivity of the interferometer may vary significantly from one energy bin to another, the signal and noise may not be separated well using the previously proposed method, therefore the full potential of the SVD method may not be achieved. This work presents a weighted SVD-based method, which maintains the noise reduction capability regardless of the similarity in the noise level across energy bins. The optimal weighting scheme was theoretically derived, and experimental phantom studies were performed to validate the theory and demonstrate the improved radiation dose efficiency of the proposed weighted SVD method.