Task-Driven Adaptive Statistical Compressive Sensing of Gaussian Mixture Models

TL;DR

This paper introduces a task-driven adaptive compressive sensing framework for Gaussian mixture models that optimizes sensing protocols for classification and reconstruction, demonstrating improved performance over standard methods.

Contribution

It develops a novel adaptive sensing paradigm based on information theory tailored for GMMs, enabling joint class detection and signal reconstruction.

Findings

Enhanced classification accuracy with adaptive sensing

Improved reconstruction quality over standard protocols

Effective across synthetic, satellite, and natural image data

Abstract

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.