C-arm cone-beam CT (CBCT) can provide intraoperative 3D imaging capability for surgical guidance, but workflow and radiation dose are the significant barriers to broad utilization. One main reason is that each 3D image acquisition requires a complete scan with a full radiation dose to present a completely new 3D image every time. In this paper, we propose to utilize patient-specific CT or CBCT as prior knowledge to accurately reconstruct the aspects of the region that have changed by the surgical procedure from only a sparse set of x-rays. The proposed methods consist of a 3D-2D registration between the prior volume and a sparse set of intraoperative x-rays, creating digitally reconstructed radiographs (DRRs) from the registered prior volume, computing difference images by subtracting DRRs from the intraoperative x-rays, a penalized likelihood reconstruction of the volume of change (VOC) from the difference images, and finally a fusion of VOC reconstruction with the prior volume to visualize the entire surgical field. When the surgical changes are local and relatively small, the VOC reconstruction involves only a small volume size and a small number of projections, allowing less computation and lower radiation dose than is needed to reconstruct the entire surgical field. We applied this approach to sacroplasty phantom data obtained from a CBCT test bench and vertebroplasty data with a fresh cadaver acquired from a C-arm CBCT system with a flat-panel detector. The VOCs were reconstructed from a varying number of images (10-66 images) and compared to the CBCT ground truth using four different metrics (mean squared error, correlation coefficient, structural similarity index and perceptual difference model). The results show promising reconstruction quality with structural similarity to the ground truth close to 1 even when only 15-20 images were used, allowing dose reduction by the factor of 10-20.