Computational periscopy with an ordinary digital camera

Computing the amounts of light arriving from different directions enables a diffusely reflecting surface to play the part of a mirror in a periscope—that is, perform non-line-of-sight imaging around an obstruction. Because computational periscopy has so far depended on light-travel distances being proportional to the times of flight, it has mostly been performed with expensive, specialized ultrafast optical systems^1,2,3,4,5,6,7,8,9,10,11,12. Here we introduce a two-dimensional computational periscopy technique that requires only a single photograph captured with an ordinary digital camera. Our technique recovers the position of an opaque object and the scene behind (but not completely obscured by) the object, when both the object and scene are outside the line of sight of the camera, without requiring controlled or time-varying illumination. Such recovery is based on the visible penumbra of the opaque object having a linear dependence on the hidden scene that can be modelled through ray optics. Non-line-of-sight imaging using inexpensive, ubiquitous equipment may have considerable value in monitoring hazardous environments, navigation and detecting hidden adversaries.We thank F. Durand, W. T. Freeman, Y. Ma, J. Rapp, J. H. Shapiro, A. Torralba, F. N. C. Wong and G. W. Wornell for discussions. This work was supported by the Defense Advanced Research Projects Agency (DARPA) REVEAL Program contract number HR0011-16-C-0030. (HR0011-16-C-0030 - Defense Advanced Research Projects Agency (DARPA) REVEAL Program)Accepted manuscrip

Sensing physical fields: Inverse problems for the diffusion equation and beyond

Due to significant advances made over the last few decades in the areas of (wireless) networking, communications and microprocessor fabrication, the use of sensor networks to observe physical phenomena is rapidly becoming commonplace. Over this period, many aspects of sensor networks have been explored, yet a thorough understanding of how to analyse and process the vast amounts of sensor data collected, remains an open area of research. This work therefore, aims to provide theoretical, as well as practical, advances this area. In particular, we consider the problem of inferring certain underlying properties of the monitored phenomena, from our sensor measurements. Within mathematics, this is commonly formulated as an inverse problem; whereas in signal processing it appears as a (multidimensional) sampling and reconstruction problem. Indeed it is well known that inverse problems are notoriously ill-posed and very demanding to solve; meanwhile viewing it as the latter also presents several technical challenges. In particular, the monitored field is usually nonbandlimited, the sensor placement is typically non-regular and the space-time dimensions of the field are generally non-homogeneous. Furthermore, although sensor production is a very advanced domain, it is near impossible and/or extremely costly to design sensors with no measurement noise. These challenges therefore motivate the need for a stable, noise robust, yet simple sampling theory for the problem at hand. In our work, we narrow the gap between the domains of inverse problems and modern sampling theory, and in so doing, extend existing results by introducing a framework for solving the inverse source problems for a class of some well-known physical phenomena. Some examples include: the reconstruction of plume sources, thermal monitoring of multi-core processors and acoustic source estimation, to name a few. We assume these phenomena and their sources can be described using partial differential equation (PDE) and parametric source models, respectively. Under this assumption, we obtain a well-posed inverse problem. Initially, we consider a phenomena governed by the two-dimensional diffusion equation -- i.e. 2-D diffusion fields, and assume that we have access to its continuous field measurements. In this setup, we derive novel exact closed-form inverse formulae that solve the inverse diffusion source problem, for a class of localized and non-localized source models. In our derivation, we prove that a particular 1-D sequence of, so called, generalized measurements of the field is governed by a power-sum series, hence it can be efficiently solved using existing algebraic methods such as Prony's method. Next, we show how to obtain these generalized measurements, by using Green's second identity to combine the continuous diffusion field with a family of well-chosen sensing functions. From these new inverse formulae, we therefore develop novel noise robust centralized and distributed reconstruction methods for diffusion fields. Specifically, we extend these inverse formulae to centralized sensor networks using numerical quadrature; conversely for distributed networks, we propose a new physics-driven consensus scheme to approximate the generalized measurements through localized interactions between the sensor nodes. Finally we provide numerical results using both synthetic and real data to validate the proposed algorithms. Given the insights gained, we eventually turn to the more general problem. That is, the two- and three-dimensional inverse source problems for any linear PDE with constant coefficients. Extending the previous framework, we solve the new class of inverse problems by establishing an otherwise subtle link with modern sampling theory. We achieved this by showing that, the desired generalized measurements can be computed by taking linear weighted-sums of the sensor measurements. The advantage of this is two-fold. First, we obtain a more flexible framework that permits the use of more general sensing functions, this freedom is important for solving the 3-D problem. Second, and remarkably, we are able to analyse many more physical phenomena beyond diffusion fields. We prove that computing the proper sequence of generalized measurements for any such field, via linear sums, reduces to approximating (a family of) exponentials with translates of a particular prototype function. We show that this prototype function depends on the Green's function of the field, and then derive an explicit formula to evaluate the proper weights. Furthermore, since we now have more freedom in selecting the sensing functions, we discuss how to make the correct choice whilst emphasizing how to retrieve the unknown source parameters from the resulting (multidimensional) Prony-like systems. Based on this new theory we develop practical, noise robust, sensor network strategies for solving the inverse source problem, and then present numerical simulation results to verify the performance of our proposed schemes.Open Acces

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

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

Source shot noise mitigation in scanned beam microscopy

Accepted manuscrip

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

Regional Economic Implications of Water Allocation and Reliability

The understanding of how allocation decisions can maximise the economic returns to the community from water for irrigation has received little attention, but is a significant issue for regional councils, those interested in water allocation policy development, and for irrigated farmers. There is a tradeoff between the amount of irrigated area and the reliability with which it can be undertaken. Overseas studies have generated a curve with optimum levels of allocation which maximise the economic return to the community from the resource. The study on which this paper is based used a single case study to model the individual and regional economic outcomes for four scenarios of water allocation, using daily time step simulation models of the hydrological, irrigation, farm and financial systems over the 1973 – 2000 period. The results show that there is an increasing return to the region as the allocation from the resource increases, at the expense of lower returns to existing users.Irrigation, reliability, regional economic impacts, Agribusiness, Agricultural and Food Policy, Agricultural Finance, Community/Rural/Urban Development, Environmental Economics and Policy, Farm Management, Financial Economics, Institutional and Behavioral Economics, Land Economics/Use, Resource /Energy Economics and Policy,

Impact of Burkholderia Infection on Lung Transplantation in Cystic Fibrosis

Rationale: Lung transplantation offers the only survival option for patients with cystic fibrosis (CF) with end-stage pulmonary disease. Infection with Burkholderia species is typically considered a contraindication to transplantation in CF. However, the risks posed by different Burkholderia species on transplantation outcomes are poorly defined. Objectives: To quantify the risks of infection with Burkholderia species on survival before and after lung transplantation in patients with CF. Methods: Multivariate Cox survival models assessed hazard ratios of infection with Burkholderia species in 1,026 lung transplant candidates and 528 lung transplant recipients. Lung allocation scores, incorporating Burkholderia infection status, were calculated for transplant candidates. Measurements and Main Results: Transplant candidates infected with different Burkholderia species did not have statistically different mortality rates. Among transplant recipients infected with B. cenocepacia, only those infected with nonepidemic strains had significantly greater post-transplant mortality compared with uninfected patients (hazard ratio [HR], 2.52; 95% confidence interval [CI], 1.04–6.12; P 5 0.04). Hazards were similar between uninfected transplant recipients and those infected with B. multivorans (HR, 0.66; 95% CI, 0.27–1.56; P 5 0.34). Transplant recipients infected with B. gladioli had significantly greater post-transplant mortality than uninfected patients (HR, 2.23; 95% CI, 1.05–4.74; P 5 0.04). Oncehazards for species/strainwereincluded,lung allocation scores of B. multivorans–infected transplant candidates were comparable to uninfected candidate scores, whereas those of candidates infected with nonepidemic B. cenocepacia or B. gladioli were lower. Conclusions: Post-transplant mortality among patients with CF infected with Burkholderia varies by infecting species. This variability should be taken into account in evaluating lung transplantation candidates.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91898/1/Murray LiPuma AJRCCM 2008.pd

Carlsberg alibi marketing in the UEFA Euro 2016 football finals: implications of Probably inappropriate alcohol advertising

Background: Alcohol advertising is a key driver of alcohol consumption, and is prohibited in France by the Loi Evin. In 2016 the Danish brewer Carlsberg sponsored the UEFA Euro 2016 finals, held in France, and used the alibis ‘Probably’ and ‘…the best in the world’ in place of Carlsberg in pitch-side advertising. We have quantified the advertising exposure achieved during the final seven games in the UEFA Euro 2016 championship. Methods: Appearances of the Carlsberg alibis ‘Probably’ and ‘the best in the world’ were counted and timed to the nearest second during all active play in live coverage of quarter final, semi-final and final matches broadcast in the UK. We used census data and viewing figures from Kantar Media to estimate gross and per capita impressions of these advertisements in the UK population. Results: In 796 minutes, 29 seconds of active play there were 746 alibi appearances, totalling 68 minutes 35 seconds duration and representing 8.6% of active playing time. Appearances were particularly frequent at the end of normal time, extra time and penalties. The seven matches delivered up to 7.43 billion Carlsberg alibi impressions to UK adults and 163.3 million to children. In the only match involving a second country with laws prohibiting alcohol advertising (France versus Iceland), exposure occurred for only 1.8% of playing time. Conclusions: Alibi marketing achieved significant advertising coverage during the final seven EURO 2016 championship games, particularly to children. Since ‘Probably’ is registered by Carlsberg as a wordmark this advertising appears to contravene the Loi Evin, though Carlsberg have defended their marketing actions