An iterative gradient convolutional neural network and its application in endoscopic photoacoustic image formation from incomplete acoustic measurement

Endoscopic photoacoustic tomography (EPAT) is a rapidly developing catheter-based imaging technique to provide cross-sectional images of anatomical, functional and molecular data of tubular objects. The scanning geometry of the ultrasonic detector is enclosed in the cavity resulting in highly restricted acquisition of photoacoustically induced acoustic pressures. Thus, data-incompleteness is an important factor that causes degradation of the image quality. This work presents a method to solve the acoustic inverse problem of EPAT from incomplete measurements associated with the image formation process. This method combines the traditional variational iteration with convolutional neural network (CNN), in which the forward operator and adjoint operator of imaging are excluded from the network training and are embedded into each layer of the structural unit. The gradient information is utilized to reduce the influence of incomplete measurements on the image quality. The network is trained unit by unit in an adaptive way to achieve fast convergence. Our numerical results conducted on various data sets showed that the trained network is robust to the sampling rate of the measured data. Also, it is able to provide a generalization that can work across various noise levels in the data. In addition, a robust peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) improvement obtained in the reconstructed images has been demonstrated in comparison with conventional TR reconstruction, CS reconstruction and post-processing by U-net.