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Imaging through a strongly diffusive medium remains an outstanding challenge, in particular in applications in biological and medical imaging. Here, we propose a method based on a single-photon time-of-flight camera that allows, in combination with computational processing of the spatial and full temporal photon distribution data, imaging of an object embedded inside a strongly diffusive medium over more than 80 transport mean free paths. The technique is contactless and requires 1 s acquisition times, thus allowing Hz frame rate imaging. The imaging depth corresponds to several centimetres of human tissue and allows us to perform deep-body imaging as a proof of principle. By combining a single-photon time-of-flight camera with computational processing of the spatial and full temporal photon distribution data, an object embedded inside a strongly diffusive medium can be imaged over more than 80 transport mean free paths in a contactless manner on the timescale of the order of 1 s. [ABSTRACT FROM AUTHOR]

A number of recent works have emphasized the prominent role played by the Kurdyka-Łojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of two terms: (i) a differentiable, but not necessarily convex, function and (ii) a function that is not necessarily convex, nor necessarily differentiable. The latter function is expressed as a separable sum of functions of blocks of variables. Such an optimization problem can be addressed with the Forward-Backward algorithm which can be accelerated thanks to the use of variable metrics derived from the Majorize-Minimize principle. We propose to combine the latter acceleration technique with an alternating minimization strategy which relies upon a flexible update rule. We give conditions under which the sequence generated by the resulting Block Coordinate Variable Metric Forward-Backward algorithm converges to a critical point of the objective function. An application example to a nonconvex phase retrieval problem encountered in signal/image processing shows the efficiency of the proposed optimization method. [ABSTRACT FROM AUTHOR]

We consider the minimization of a function G defined on ${ \mathbb{R} } ^{N}$, which is the sum of a (not necessarily convex) differentiable function and a (not necessarily differentiable) convex function. Moreover, we assume that G satisfies the Kurdyka-Łojasiewicz property. Such a problem can be solved with the Forward-Backward algorithm. However, the latter algorithm may suffer from slow convergence. We propose an acceleration strategy based on the use of variable metrics and of the Majorize-Minimize principle. We give conditions under which the sequence generated by the resulting Variable Metric Forward-Backward algorithm converges to a critical point of G. Numerical results illustrate the performance of the proposed algorithm in an image reconstruction application. [ABSTRACT FROM AUTHOR]

The thin and flexible nature of optical fibres often makes them the ideal technology to view biological processes in-vivo, but current microendoscopic approaches are limited in spatial resolution. Here, we demonstrate a route to high resolution microendoscopy using a multicore fibre (MCF) with an adiabatic multimode-to-single-mode "photonic lantern" transition formed at the distal end by tapering. We show that distinct multimode patterns of light can be projected from the output of the lantern by individually exciting the single-mode MCF cores, and that these patterns are highly stable to fibre movement. This capability is then exploited to demonstrate a form of single-pixel imaging, where a single pixel detector is used to detect the fraction of light transmitted through the object for each multimode pattern. A custom computational imaging algorithm we call SARA-COIL is used to reconstruct the object using only the pre-measured multimode patterns themselves and the detector signals. Here, the authors demonstrate a route to high resolution microendoscopy using a multicore fibre with a photonic lantern. They show that distinct multimode patterns of light can be projected from the output of the lantern by individually exciting the single-mode MCF cores, whose patterns are highly stable to fibre movement. [ABSTRACT FROM AUTHOR]