Optimal stopping times for estimating Bernoulli parameters with applications to active imaging

We address the problem of estimating the parameter of a Bernoulli process. This arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. We introduce a framework within which to minimize the mean-squared error (MSE) subject to an upper bound on the mean number of trials. This optimization has several simple and intuitive properties when the Bernoulli parameter has a beta prior. In addition, by exploiting typical spatial correlation using total variation regularization, we extend the developed framework to a rectangular array of Bernoulli processes representing the pixels in a natural scene. In simulations inspired by realistic active imaging scenarios, we demonstrate a 4.26 dB reduction in MSE due to the adaptive acquisition, as an average over many independent experiments and invariant to a factor of 3.4 variation in trial budget.Accepted manuscrip

Quantum Theory of Superresolution for Two Incoherent Optical Point Sources

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern farfield superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation from the far field almost as precisely as conventional methods do for isolated sources, rendering Rayleigh's criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.Comment: 18 pages, 11 figures. v1: First draft. v2: Improved the presentation and added a section on the issues of unknown centroid and misalignment. v3: published in Physical Review

An in vivo biosensor for neurotransmitter release and in situ receptor activity.

Tools from molecular biology, combined with in vivo optical imaging techniques, provide new mechanisms for noninvasively observing brain processes. Current approaches primarily probe cell-based variables, such as cytosolic calcium or membrane potential, but not cell-to-cell signaling. We devised cell-based neurotransmitter fluorescent engineered reporters (CNiFERs) to address this challenge and monitor in situ neurotransmitter receptor activation. CNiFERs are cultured cells that are engineered to express a chosen metabotropic receptor, use the G(q) protein-coupled receptor cascade to transform receptor activity into a rise in cytosolic [Ca(2+)] and report [Ca(2+)] with a genetically encoded fluorescent Ca(2+) sensor. The initial realization of CNiFERs detected acetylcholine release via activation of M1 muscarinic receptors. We used chronic implantation of M1-CNiFERs in frontal cortex of the adult rat to elucidate the muscarinic action of the atypical neuroleptics clozapine and olanzapine. We found that these drugs potently inhibited in situ muscarinic receptor activity

Rule learning enhances structural plasticity of long-range axons in frontal cortex.

Rules encompass cue-action-outcome associations used to guide decisions and strategies in a specific context. Subregions of the frontal cortex including the orbitofrontal cortex (OFC) and dorsomedial prefrontal cortex (dmPFC) are implicated in rule learning, although changes in structural connectivity underlying rule learning are poorly understood. We imaged OFC axonal projections to dmPFC during training in a multiple choice foraging task and used a reinforcement learning model to quantify explore-exploit strategy use and prediction error magnitude. Here we show that rule training, but not experience of reward alone, enhances OFC bouton plasticity. Baseline bouton density and gains during training correlate with rule exploitation, while bouton loss correlates with exploration and scales with the magnitude of experienced prediction errors. We conclude that rule learning sculpts frontal cortex interconnectivity and adjusts a thermostat for the explore-exploit balance

Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation

Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires a simple trial allocation gain quantity. Motivated by realizing this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements: up to 4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.Comment: 13 pages, 16 figure

Beyond binomial and negative binomial: adaptation in Bernoulli parameter estimation

Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes (e.g., multiple pixels) are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires the introduction of a simple trial allocation gain quantity. Motivated by achieving this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements up to 4.36 dB for the estimation of p and up to 1.86 dB for the estimation of log p.https://arxiv.org/abs/1809.08801https://arxiv.org/abs/1809.08801First author draf