Computed tomography (CT) is one of the most widely used medical imaging modality. However, substantial x-ray dose exposed to the human subject during the CT scan is a great concern. Region-of-interest (ROI) CT is considered to be a possible solution for its potential to reduce the x-ray dose to the human subject. In most of ROI-CT scans, the ROI is set to a circular shape whose diameter is often considerably smaller than the full field-of-view (FOV). However, an arbitrarily shaped ROI is very desirable to reduce the x-ray dose more than the circularly shaped ROI can do. We propose a new method to make a non-circular convex-shaped ROI along with the image reconstruction method. To make a ROI with an arbitrary convex shape, dynamic collimations are necessary to minimize the x-ray dose at each angle of view. In addition to the dynamic collimation, we get the ROI projection data with slightly lower sampling rate in the view direction to further reduce the x-ray dose. We reconstruct images from the ROI projection data in the compressed sensing (CS) framework assisted by the exterior projection data acquired from the pilot scan to set the ROI. To validate the proposed method, we used the experimental micro-CT projection data after truncating them to simulate the dynamic collimation. The reconstructed ROI images showed little errors as compared to the images reconstructed from the full-FOV scan data as well as little artifacts inside the ROI. We expect the proposed method can significantly reduce the x-ray dose in CT scans if the dynamic collimation is realized in real CT machines.