Imaging complex targets through alphabet-based compressive sensing

Imaging techniques exploiting sparseness-regularized formulations emerged in the last few years as powerful and effective retrieval methods in several heterogeneous scenarios [1] including structural monitoring, non-destructive testing and evaluation, ground penetrating radar imaging, and biomedical diagnosis [2–8]. The success of the this class of algorithms, which are often collectively indicated as Compressive Sensing (CS) [9], is motivated by several concurring factors, including their accuracy, robustness, numerical efficiency, capability to handle several different contexts (e.g., including transverse-magnetic [2] and transverse-electric problems [3], single-/multi-frequency data [2, 4], isotropic/anisotropic media [1]) in a seamless way, and the availability of efficient implementations of many different solvers [1]. On the other hand, CS techniques are not general-purpose imaging algorithms. Their application requires the problem at hand to comply with some fundamental assumptions [1], including the fact that the unknown (e.g., the contrast [8] or equivalent currents [9]) is sparse in the employed basis. Early applications of CS methods, which used simple pixel-bases to expand the unknowns, addressed only those scenarios were the object is composed by few isolated pixels [2]. Nevertheless, it is well known that sparsity is not an absolute concept, but it is always in relation with the representation basis [1]. The use of different expansion bases [10] has been then proposed to enable more complex profiles to be imaged [7]. Unfortunately, such techniques always assume that some knowledge on the target profile is available, so that this a-priori information can be exploited to define the most suitable expansion basis to be adopted [7]. A different perspective is considered in this paper to enable the application of CS methodologies when no prior information on the class of targets under investigation is available. More specifically, a large alphabet of candidate bases is generated off-line, and for each basis a candidate reconstructions are carried out in parallel “online” by the CS retrieval tool. The retrieved profiles are then compared, and a sparsity-based criterion is adopted in turns to select the most reliable reconstruction (among those obtained by the different bases). Preliminary numerical experiments will be shown to assess the accuracy and numerical efficiency of the proposed imaging methodology.