Principles of Modern Radar - Volume 2 1891121537

184 CHAPTER 5 Radar Applications of Sparse Reconstructioncoefficients. 37 On the other hand, Patel et al. [136] compare various randomized slowtimeundersampling schemes, which advantageously enable the SAR to reduce its overallduty cycle by skipping pulses.Another potential problem is in the direct measurement of wideband signals; when thenarrowband approximation is insufficient, standard baseband processing cannot be used toease analog-to-digital conversion (ADC); thus many state-of-the-art radars are beginningto push the limits of ADC hardware. Baraniuk [137] and Romberg [138] suggest thepossibility of randomly undersampling each pulse in fast time, thereby reducing the loadon the ADC with the assumption that each pulse is compressible in a known basis suchas the point-scatterer dictionary. For an example paper considering analog, that is, infinitedimensional signals, from a CS perspective, see [139].A substantial percentage of radar problems are concerned with obtaining better performance(in terms of, for example, target detections, image resolution) with the samedata; that is, the waveforms and acquisition strategy have already been chosen and there isno need to throw away precious data, but we still would like to exploit the underlying datasparsity for a given problem. An example of such work is the PhD research of Cetin [75],which employed various non quadratically constrained reconstructions schemes (TV, l p ,etc.) in order to improve SAR image quality with data collected from DARPA’s Movingand Stationary Target Acquisition and Recognition (MSTAR) program [140]. Many ofthe application-inspired SR techniques exploit structured sparsity. Significant examplesinclude the work of Varshney et al. [141], which develops a greedy approach for reconstructingradar signals composed of anisotropic scattering centers, Cevher et al. [113], whoemploy quadtree graphical models for sparse reconstruction of SAR images, as well asDuarte and Baraniuk [59], who have developed MUSIC-based techniques that significantlyoutperform standard SR algorithms for the problem of estimating sinusoids in noise.It should be noted that one often desires a measure of confidence in a given image. Asdiscussed in Section 5.3.5, the Bayesian framework enables us to estimate posterior probabilitiesfor reconstructed images. Algorithms for obtaining radar images with confidencelabels include, for example, the fast Bayesian matching pursuits (FBMP) approach bySchniter et al. [97] and Bayesian compressive sensing (BCS) algorithm by Ji et al. [142].Here we illustrate five different radar applications in which SR can improve imagequality, the fifth of which is an application of CS. The first is a moving-target imagingexample in which the target is undergoing random motion that is representative of therelative motion between a target moving down a dirt road and a SAR antenna flyingalong a planned linear trajectory. The second example demonstrates the use of SR inthe case of a civilian vehicle; in order to efficiently model the data, dictionary elementswith an anisotropic angular response are required. The third example shows how theconglomeration of physically meaningful regularization terms (l 1 , l 2 , and TV) can obtainexcellent imaging results for imaging underground scenes. The last imaging exampleshows how SR can be utilized in the nonlinear setting, that is, without invoking eitherof the Born or Rytov approximations, by solving the far-field relation used in the linearsampling method (LSM). The final example demonstrates how the transmitted waveformcan be designed to make the scattered data more amenable to sparse reconstruction in therange-Doppler plane.37 It is perhaps useful to note that [135] gauged the image-compression performance by the quality ofcoherent change detection (CCD) imagery.