Compressive phase-only filtering at extreme compression rates

TL;DR

This paper presents a fast, efficient method for reconstructing correlations between compressively measured images and phase-only filters, enabling target recognition at extremely high compression rates without prior knowledge of the target.

Contribution

It introduces a novel approach leveraging phase-only filter properties for compressive sensing, allowing accurate correlation-based recognition directly from highly compressed data.

Findings

Effective at very high compression rates

Enables target classification without full image reconstruction

Applicable to single-pixel camera measurements

Abstract

We introduce an efficient method for the reconstruction of the correlation between a compressively measured image and a phase-only filter. The proposed method is based on two properties of phase-only filtering: such filtering is a unitary circulant transform, and the correlation plane it produces is usually sparse. Thanks to these properties, phase-only filters are perfectly compatible with the framework of compressive sensing. Moreover, the lasso-based recovery algorithm is very fast when phase-only filtering is used as the compression matrix. The proposed method can be seen as a generalisation of the correlation-based pattern recognition technique, which is hereby applied directly to non-adaptively acquired compressed data. At the time of measurement, any prior knowledge of the target object for which the data will be scanned is not required. We show that images measured at extremely high compression rates may still contain sufficient information for target classification and localization, even if the compression rate is high enough, that visual recognition of the target in the reconstructed image is no longer possible. The method has been applied by us to highly undersampled measurements obtained from a single-pixel camera, with sampling based on randomly chosen Walsh-Hadamard patterns.