Improved Radon Based Imaging using the Shearlet Transform

摘要

Many imaging modalities, such as Synthetic Aperture Radar (SAR), can be described mathematically as collecting data in a Radon transform domain. The process of inverting the Radon transform to form an image can be unstable when the data collected contain noise so that the inversion needs to be regularized in some way. In this work, we develop a method for inverting the Radon transform using a shearlet-based decomposition, which provides a regularization that is nearly optimal for a general class of images. We then show through a variety of examples that this technique performs better than similar competitive methods based on the use of the wavelet and the curvelet transforms.