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In many surveillance applications, high resolution imaging sensors provide imagery over large areas for operators to visually determine the presence of threats. Two significant challenges are: 1) the large amount of image data can be taxing for a human operator over a long period of time (as well as for other system resources such as network bandwidth), and 2) relatively expensive optics and large focal plane arrays are needed to produce high quality images. Compressed sensing holds the promise for radically novel sensors that can perfectly reconstruct images using comparatively simple hardware and considerably fewer samples of data than required by the otherwise general Shannon sampling theorem. It has been shown by Candes, Romberg, and Tao, Donoho, and others that by measuring relatively few projections of a scene on random vectors, iterative greedy algorithms and basis pursuit techniques that minimize the L1 norm of the solution vector can perfectly reconstruct the entire image. To reduce the load on the human operator, however, it is also desirable to cue regions of the image where objects of interest may exist. Towards this end, we are interested here in selectively imaging interesting objects in a scene, without necessarily seeking perfect reconstruction of the whole image. We show that our goals are achieved by minimizing a modified L2-norm criterion when the reconstruction of only specific objects is of interest. We achieve this by introducing prior knowledge about objects in a known basis as soft constraints in the reconstruction equation. At first blush it may appear that the same could be achieved by measuring projections of the objects directly on the basis set. However, this trivial solution requires that the basis functions be changed for every object; thus, the solution is not suitable for practical applications. We show that the proposed approach takes advantage of the simplicity, elegance, and generality of the compressed sensing architecture by ach- ieving object-specific reconstruction using random projection on simple binary masks. Most importantly, a single set of random projective measurements can be used to algorithmically reconstruct any object of interest without requiring explicit and repeated measurements on different basis sets that vary with the object of interest. Clearly, this has significant implications on system issues and practical consideration such as hardware complexity and time required for searching for objects over a large number of classes. Our assumption that some information is known about specific objects of interest is distinctly different from the original theory of compressed sensing as postulated by Candes, et al. and Donoho. The proposed method is not an alternative when the perfect reconstruction of arbitrary images is required, but nevertheless operates within the same framework by extracting information from compressive measurements. The proposed method yields a simple closed-form analytical solution that does not require iterative processing. Objects can be meaningfully sensed in considerable detail while heavily compressing the scene elsewhere. Essentially, this embeds the object detection and clutter discrimination function in the sensing and imaging process. To the best of our knowledge, this is the first application of a compressed sensing architecture that is explicitly tailored for surveillance scenarios where the ability to find specific objects is of interest.
Aerospace and Electronic Systems, IEEE Transactions on (Volume:45 , Issue: 3 )
Date of Publication: July 2009