Locating salient group-structured image features via adaptive compressive sensing

In this paper we consider the task of locating salient group-structured features in potentially high-dimensional images; the salient feature detection here is modeled as a Robust Principal Component Analysis problem, in which the aim is to locate groups of outlier columns embedded in an otherwise low rank matrix. We adapt an adaptive compressive sensing method from our own previous work (which examined the task of identifying arbitrary sets of outlier columns in large matrices) to settings where the outlier columns occur in groups, and establish theoretical results certifying that accurate group-structured inference is achievable using very few linear measurements of the image, subject to some (arguably) minor structural assumptions on the image itself. We also demonstrate, through extensive numerical simulations, our proposed algorithm in a salient object detection task, and show that it simultaneously achieves low sample and computational complexity, while exhibiting performance comparable to state-of-the-art methods that acquire and process the entire image.