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We describe a foveated compressive sensing approach for image analysis applications that utilizes knowledge of the task to be performed to reduce the number of required measurements compared to conventional Nyquist sampling and compressive sensing based approaches. Our Compressive Optical Foveated Architecture (COFA) adapts the dictionary and compressive measurements to structure and sparsity in the signal, task, and scene by reducing measurement and dictionary mutual coherence and increasing sparsity using principles of actionable information and foveated compressive sensing. Actionable information is used to extract task-relevant regions of interest (ROIs) from a low-resolution scene analysis by eliminating the effects of nuisances for occlusion and anomalous motion detection. From the extracted ROIs, preferential measurements are taken using foveation as part of the compressive sensing adaptation process. The task-specific measurement matrix is optimized by using a novel saliency-weighted coherence minimization with respect to the learned signal dictionary. This incorporates the relative usage of the atoms in the dictionary. Therefore, the measurement matrix is not random, as in conventional compressive sensing, but is based on the dictionary structure and atom distributions. We utilize a patch-based method to learn the signal priors. A treestructured dictionary of image patches using KSVD is learned which can sparsely represent any given image patch with the tree-structure. We have implemented COFA in an end-to-end simulation of a vehicle fingerprinting task for aerial surveillance using foveated compressive measurements adapted to hierarchical ROIs consisting of background, roads, and vehicles. Our results show 113x reduction in measurements over conventional sensing and 28x reduction over compressive sensing using random measurements.
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