Quantum-inspired computational imaging

Computational imaging combines measurement and computational methods with the aim of forming images even when the measurement conditions are weak, few in number, or highly indirect. The recent surge in quantum-inspired imaging sensors, together with a new wave of algorithms allowing on-chip, scalable and robust data processing, has induced an increase of activity with notable results in the domain of low-light flux imaging and sensing. We provide an overview of the major challenges encountered in low-illumination (e.g., ultrafast) imaging and how these problems have recently been addressed for imaging applications in extreme conditions. These methods provide examples of the future imaging solutions to be developed, for which the best results are expected to arise from an efficient codesign of the sensors and data analysis tools.Y.A. acknowledges support from the UK Royal Academy of Engineering under the Research Fellowship Scheme (RF201617/16/31). S.McL. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grant EP/J015180/1). V.G. acknowledges support from the U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office award W911NF-10-1-0404, the U.S. DARPA REVEAL program through contract HR0011-16-C-0030, and U.S. National Science Foundation through grants 1161413 and 1422034. A.H. acknowledges support from U.S. Army Research Office award W911NF-15-1-0479, U.S. Department of the Air Force grant FA8650-15-D-1845, and U.S. Department of Energy National Nuclear Security Administration grant DE-NA0002534. D.F. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grants EP/M006514/1 and EP/M01326X/1). (RF201617/16/31 - UK Royal Academy of Engineering; EP/J015180/1 - UK Engineering and Physical Sciences Research Council; EP/M006514/1 - UK Engineering and Physical Sciences Research Council; EP/M01326X/1 - UK Engineering and Physical Sciences Research Council; W911NF-10-1-0404 - U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office; HR0011-16-C-0030 - U.S. DARPA REVEAL program; 1161413 - U.S. National Science Foundation; 1422034 - U.S. National Science Foundation; W911NF-15-1-0479 - U.S. Army Research Office; FA8650-15-D-1845 - U.S. Department of the Air Force; DE-NA0002534 - U.S. Department of Energy National Nuclear Security Administration)Accepted manuscrip

From cognitive science to cognitive neuroscience to neuroeconomics

As an emerging discipline, neuroeconomics faces considerable methodological and practical challenges. In this paper, I suggest that these challenges can be understood by exploring the similarities and dissimilarities between the emergence of neuroeconomics and the emergence of cognitive and computational neuroscience two decades ago. From these parallels, I suggest the major challenge facing theory formation in the neural and behavioural sciences is that of being under-constrained by data, making a detailed understanding of physical implementation necessary for theory construction in neuroeconomics. Rather than following a top-down strategy, neuroeconomists should be pragmatic in the use of available data from animal models, information regarding neural pathways and projections, computational models of neural function, functional imaging and behavioural data. By providing convergent evidence across multiple levels of organization, neuroeconomics will have its most promising prospects of success

Convergence of Entropic Schemes for Optimal Transport and Gradient Flows

Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach has recently been used successfully to solve optimal transport related problems in several applied fields such as imaging sciences, machine learning and social sciences. The main reason for this success is that, in contrast to linear programming solvers, the resulting algorithms are highly parallelizable and take advantage of the geometry of the computational grid (e.g. an image or a triangulated mesh). The first contribution of this article is the proof of the $\Gamma$-convergence of the entropic regularized optimal transport problem towards the Monge-Kantorovich problem for the squared Euclidean norm cost function. This implies in particular the convergence of the optimal entropic regularized transport plan towards an optimal transport plan as the entropy vanishes. Optimal transport distances are also useful to define gradient flows as a limit of implicit Euler steps according to the transportation distance. Our second contribution is a proof that implicit steps according to the entropic regularized distance converge towards the original gradient flow when both the step size and the entropic penalty vanish (in some controlled way)

Applications of MATLAB in Natural Sciences: A Comprehensive Review

In the natural sciences, MATLAB is a versatile and essential tool that has revolutionized research across various disciplines, including physics, chemistry, biology, geology, and environmental sciences. This review paper provides a comprehensive overview of MATLAB's applications in data analysis, modeling, simulation, image processing, computational chemistry, environmental sciences, physics, engineering, and data visualization. MATLAB simplifies data analysis by handling complex datasets, performing statistical analyses, and aiding in tasks like curve fitting and spectral analysis. In modeling and simulation, it enables the creation of predictive models for intricate systems, facilitating simulations of physical processes, ecological dynamics, and chemical reactions. In image processing, MATLAB enhances and analyzes images, benefiting fields such as medical imaging and remote sensing. For computational chemistry, MATLAB offers a rich library of tools for exploring molecular structures and simulating chemical reactions. Environmental sciences rely on MATLAB for climate data analysis and ecological modeling. In physics and engineering, it is invaluable for simulating complex systems and analyzing experimental data. Additionally, MATLAB's data visualization capabilities allow scientists to create compelling visuals for effective communication. While challenges like licensing costs exist, efforts are underway to address these issues and enhance integration with other software, including artificial intelligence and machine learning tools. Overall, MATLAB's computational power and versatility are fundamental to advancing natural sciences research, making it an invaluable resource for scientists and researchers across various disciplines

Proximal nested sampling with data-driven priors for physical scientists

Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the imaging sciences. The purpose of this article is two-fold. First, we review proximal nested sampling in a pedagogical manner in an attempt to elucidate the framework for physical scientists. Second, we show how proximal nested sampling can be extended in an empirical Bayes setting to support data-driven priors, such as deep neural networks learned from training data.Comment: 9 pages, 4 figure

Ultra-fast Lensless Computational Imaging through 5D Frequency Analysis of Time-resolved Light Transport

Light transport has been analyzed extensively, in both the primal domain and the frequency domain. Frequency analyses often provide intuition regarding effects introduced by light propagation and interaction with optical elements; such analyses encourage optimal designs of computational cameras that efficiently capture tailored visual information. However, previous analyses have relied on instantaneous propagation of light, so that the measurement of the time dynamics of light–scene interaction, and any resulting information transfer, is precluded. In this paper, we relax the common assumption that the speed of light is infinite. We analyze free space light propagation in the frequency domain considering spatial, temporal, and angular light variation. Using this analysis, we derive analytic expressions for information transfer between these dimensions and show how this transfer can be exploited for designing a new lensless imaging system. With our frequency analysis, we also derive performance bounds for the proposed computational camera architecture and provide a mathematical framework that will also be useful for future ultra-fast computational imaging systems.MIT Media Lab ConsortiumNatural Sciences and Engineering Research Council of Canad

From single-molecule spectroscopy to super-resolution imaging of the neuron: a review.

For more than 20 years, single-molecule spectroscopy has been providing invaluable insights into nature at the molecular level. The field has received a powerful boost with the development of the technique into super-resolution imaging methods, ca. 10 years ago, which overcome the limitations imposed by optical diffraction. Today, single molecule super-resolution imaging is routinely used in the study of macromolecular function and structure in the cell. Concomitantly, computational methods have been developed that provide information on numbers and positions of molecules at the nanometer-scale. In this overview, we outline the technical developments that have led to the emergence of localization microscopy techniques from single-molecule spectroscopy. We then provide a comprehensive review on the application of the technique in the field of neuroscience research.This work was supported by grants from the UK Engineering and Physical Sciences Research Council (EPSRC), The Wellcome Trust, Alzheimer’s Research UK, the Medical Research Council (MRC), and the Biotechnology and Biological Sciences Resesarch Council (BBSRC)