Ashok Amit, Neifeld Mark A
Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721, USA.
J Opt Soc Am A Opt Image Sci Vis. 2011 Jun 1;28(6):1041-50. doi: 10.1364/JOSAA.28.001041.
The inherent redundancy in natural scenes forms the basis of compressive imaging where the number of measurements is less than the dimensionality of the scene. The compressed sensing theory has shown that a purely random measurement basis can yield good reconstructions of sparse objects with relatively few measurements. However, additional prior knowledge about object statistics that is typically available is not exploited in the design of the random basis. In this work, we describe a hybrid measurement basis design that exploits the power spectral density statistics of natural scenes to minimize the reconstruction error by employing an optimal combination of a nonrandom basis and a purely random basis. Using simulation studies, we quantify the reconstruction error improvement achievable with the hybrid basis for a diverse set of natural images. We find that the hybrid basis can reduce the reconstruction error up to 77% or equivalently requires fewer measurements to achieve a desired reconstruction error compared to the purely random basis. It is also robust to varying levels of object sparsity and yields as much as 40% lower reconstruction error compared to the random basis in the presence of measurement noise.
自然场景中固有的冗余性构成了压缩成像的基础，在压缩成像中，测量次数少于场景的维度。压缩感知理论表明，一个纯粹随机的测量基能够用相对较少的测量次数对稀疏物体进行良好的重建。然而，在随机基的设计中，通常可用的关于物体统计的额外先验知识并未得到利用。在这项工作中，我们描述了一种混合测量基设计，该设计通过采用非随机基和纯粹随机基的最优组合，利用自然场景的功率谱密度统计来最小化重建误差。通过模拟研究，我们量化了对于各种自然图像，使用混合基可实现的重建误差改善。我们发现，与纯粹随机基相比，混合基可将重建误差降低多达77%，或者等效地说，实现所需的重建误差需要更少的测量次数。它对不同程度的物体稀疏性也具有鲁棒性，并且在存在测量噪声的情况下，与随机基相比，重建误差降低多达40%。
