Principles of Modern Radar - Volume 2 1891121537

196 CHAPTER 5 Radar Applications of Sparse Reconstruction5.5 SUMMARYWe have shown that many common radar applications, even those that address multiplescattering,dispersive media, and other complicated propagation effects, can be expressedin the standard linear framework for which SR and CS are applicable. Several exampleswere given in which the underlying scattering phenomenology dictates that the radar dataare sparse in a known basis, motivating the use of SR and CS techniques. Although the useof SR algorithms in radar predates CS, the CS theory provides theoretical justification oftheir use by providing performance guarantees under well-defined measurement requirementssuch as the RIP and mutual coherence constraints. The measurement requirementsthemselves are often impossible to verify. However, because they are only sufficient conditionsfor guaranteed performance, in practice SR techniques work well even withoutstrictly satisfying RIC or mutual coherence bounds. An added benefit of the CS theory isthat the measurement requirements (which, when combined with SR, constitute CS) mayguide the design of future radars and data acquisition strategies to collect better data for agiven objective, as demonstrated by the waveform-design example given in the previoussection. Beyond the standard sparsity that is now commonly exploited in the literature,structured sparsity appears in a variety of radar applications and dictionaries and, when incorporatedinto the SR algorithm, can be shown to significantly improve the performanceguarantees. Advances in CS for structured, sparse data will undoubtedly play a role infuture CS applications to radar.Many radar applications are often limited by real-time requirements and large volumesof data, which until recently have made the application of SR to realistic scenarios merelya dream for practicing radar engineers. However, the recent academic interest in CS hasrapidly accelerated research in SR techniques for large-scale problems, bringing many SRand CS applications within reach. Techniques for SR range from penalized least-squarestechniques, which have excellent reconstruction performance at the expense of comparativelyhigh computational burden, to iterative thresholding algorithms that have have moderatecomputational cost while sometimes compromising their performance guarantees, togreedy approaches, which are the most computationally efficient but have the poorest performanceguarantees (unless the greedy techniques are combined with structured-sparsityconstraints, in which case they can outperform standard l 1 solvers). Many of these techniquesare grounded in a Bayesian setting and several can determine confidence levels onresulting reconstructions, which may prove extremely useful in decision tasks that rely onreconstructed images.5.6 FURTHER READINGA vast literature on CS has been published in the last several years, and new developmentsoccur on a weekly or even daily basis. An excellent tutorial on CS ideas can be found in [21].We recently coauthored [17], an article summarizing many of the same ideas contained inthis chapter, along with additional historical references and more radar examples. Anotherrecent survey of CS applications to radar, including examples on pulse compression,inverse SAR imaging, and direction of arrival estimation, can be found in [193].Finally, as alluded to already, CS is still a rapidly evolving field. The best sources forup to date information on current trends and developments can be found online. The Rice