### Abstract

We present a task-specific information (TSI) based framework for designing compressive imaging (CI) systems. The task of target detection is chosen to demonstrate the performance of the optimized CI system designs relative to a conventional imager. In our optimization framework, we first select a projection basis and then find the associated optimal photon-allocation vector in the presence of a total photon-count constraint. Several projection bases, including principal components (PC), independent components, generalized matched-filter, and generalized Fisher discriminant (GFD) are considered for candidate CI systems, and their respective performance is analyzed for the target-detection task. We find that the TSI-optimized CI system design based on a GFD projection basis outperforms all other candidate CI system designs as well as the conventional imager. The GFD-based compressive imager yields a TSI of 0.9841 bits (out of a maximum possible 1 bit for the detection task), which is nearly ten times the 0.0979 bits achieved by the conventional imager at a signal-to-noise ratio of 5.0. We also discuss the relation between the information-theoretic TSI metric and a conventional statistical metric like probability of error in the context of the target-detection problem. It is shown that the TSI can be used to derive an upper bound on the probability of error that can be attained by any detection algorithm.

Original language | English (US) |
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Pages (from-to) | 4457-4471 |

Number of pages | 15 |

Journal | Applied optics |

Volume | 47 |

Issue number | 25 |

DOIs | |

State | Published - Sep 1 2008 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Engineering (miscellaneous)
- Electrical and Electronic Engineering

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## Cite this

*Applied optics*,

*47*(25), 4457-4471. https://doi.org/10.1364/AO.47.004457