Compressive imaging: Hybrid measurement basis design

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.