Adaptive sparse optimization for coherent and quasi-stationary problems using context-based constraints

Stationarity of the sparse coefficients as well as the sparseness of their support, along with incoherence assumptions related to restricted isometry, are fundamental to compressive sensing and sparse optimization. However, scientific study of many sparse processes encountered in nature as well as engineering applications necessitates solving ill-conditioned optimization metrics and tracking rapidly fluctuating coefficients where such incoherence and stationarity assumptions are difficult to satisfy. We propose to close the gap between mathematical optimality of sparse reconstruction and practical constraints of real-world applications by combining contextual information as external constraints to the traditional sparse optimization problem. Specifically, we explore the unobservable dimensions in a coherent reconstruction problem by navigating the non-convex topography of a modified mixed norm metric proposed in earlier work. Investigations based on simulated and experimental field data are provided.