Compressive phase-only filtering at extreme compression rates
arXiv:1604.07751 · doi:10.1016/j.optcom.2016.09.024
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.
References in corpus (6)
- Ghost imaging lidar via sparsity constraints
- Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium
- Compressive adaptive computational ghost imaging
- Hybrid Optoelectronic Correlator Architecture for Shift Invariant Target Recognition
- Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging
- Computational Ghost Imaging