Task-Driven Adaptive Statistical Compressive Sensing of Gaussian Mixture Models
This work addresses the need for more efficient sensing in applications like remote sensing and imaging by adapting protocols to specific tasks, though it is incremental as it builds on existing compressive sensing frameworks.
The paper tackled the problem of designing task-specific sensing protocols for classification and reconstruction in compressive sensing by replacing sparsity with a statistical model, achieving improvements over standard protocols in experiments with synthetic signals, satellite data, and natural images under various noise levels.
A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity.