基于微分压缩感知的图像去模糊技术研究

Image deblurring based on derivative compressive sensing

尽管图像去模糊是一个病态问题,但是只要对需要恢复的图像作适当的假设就能得到唯一的稳定解。考虑了一个缺乏先验条件的图像去模糊问题,从而将图像的恢复转换为一个盲去卷积问题。作为一个特殊的应用,现有文献大多集中在受到大气扰动影响的短曝光图像的重建问题。大气扰动会使得光波产生随机偏离,从而使得光学系统的PSF产生随机变化。一种处理办法是采用自适应方法,如Shack-Hartmann干涉计。在该系统中,光波重建的准确率与干涉计所采用的透镜数成正比,从而使得计算非常复杂。采用微分压缩感知的方法,可降低透镜的数目,从而使得计算的复杂度大大降低。另一方面,利用压缩感知理论,降采样不会造成数据的丢失,从而使得光波重建的准确率能够与常规方法相同。仿真表明,采用微分压缩感知的方法能够准确地实现光波的重建,大大提高了系统的效率。

Despite its ill-posed nature, the image deblurring problem could often be solved in a unique and stable manner, provided appropriate assumptions on the nature of the images to be recovered. This paper, however, considered a more chal- lenging setting, in which accurate knowledge of the blurring operator was lacking, thereby transforming the reconstruction problem at hand into a problem of blind deconvolution. As a specific application, the current presentation focused on recon- struction of short-exposure 6ptieal images measured through atmospheric turbulence. The latter was known to give rise to ran- dom aberrations in the optical wavefront, which were in turn translated into random variations of the point spread function （PSF） of the optical system in use. It involved a standard way to track such variations using adaptive optics, for example, the Shack-Hartmann interferometer. In such a case, the accuracy of wavefront reconstruction was proportional to the number of Lenslets used by the interferometer and, hence, increased its complexity. Accordingly, this paper showed how to minimize the above complexity through reducing the number of the lenslets by means of derivative compressed sensing. Additionally, it pro- vided empirical proof that the above simplification and its associated solution scheme result in image reconstructions, whose quality was comparable to the reconstructions obtained using conventional measurements of the optical wavefront.