Single-shot compressed ultrafast photography: a review

Compressed ultrafast photography (CUP) is a burgeoning single-shot computational imaging technique that provides an imaging speed as high as 10 trillion frames per second and a sequence depth of up to a few hundred frames. This technique synergizes compressed sensing and the streak camera technique to capture nonrepeatable ultrafast transient events with a single shot. With recent unprecedented technical developments and extensions of this methodology, it has been widely used in ultrafast optical imaging and metrology, ultrafast electron diffraction and microscopy, and information security protection. We review the basic principles of CUP, its recent advances in data acquisition and image reconstruction, its fusions with other modalities, and its unique applications in multiple research fields

Inferring Sparsity: Compressed Sensing using Generalized Restricted Boltzmann Machines

In this work, we consider compressed sensing reconstruction from $M$ measurements of $K$-sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine, can be trained in an unsupervised manner on example signals, we demonstrate how this signal model can be used within a Bayesian framework of signal reconstruction. By deriving a message-passing inference for general distribution restricted Boltzmann machines, we are able to integrate these inferred signal models into approximate message passing for compressed sensing reconstruction. Finally, we show for the MNIST dataset that this approach can be very effective, even for $M < K$.Comment: IEEE Information Theory Workshop, 201

Deep learning versus ℓ1\ell^1-minimization for compressed sensing photoacoustic tomography

We investigate compressed sensing (CS) techniques for reducing the number of measurements in photoacoustic tomography (PAT). High resolution imaging from CS data requires particular image reconstruction algorithms. The most established reconstruction techniques for that purpose use sparsity and $\ell^1$-minimization. Recently, deep learning appeared as a new paradigm for CS and other inverse problems. In this paper, we compare a recently invented joint $\ell^1$-minimization algorithm with two deep learning methods, namely a residual network and an approximate nullspace network. We present numerical results showing that all developed techniques perform well for deterministic sparse measurements as well as for random Bernoulli measurements. For the deterministic sampling, deep learning shows more accurate results, whereas for Bernoulli measurements the $\ell^1$-minimization algorithm performs best. Comparing the implemented deep learning approaches, we show that the nullspace network uniformly outperforms the residual network in terms of the mean squared error (MSE).Comment: This work has been presented at the Joint Photoacoustics Session with the 2018 IEEE International Ultrasonics Symposium Kobe, October 22-25, 201

Model based learning for accelerated, limited-view 3D photoacoustic tomography

Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide high resolution 3D images from restricted photoacoustic measurements. The network is designed to represent an iterative scheme and incorporates gradient information of the data fit to compensate for limited view artefacts. Due to the high complexity of the photoacoustic forward operator, we separate training and computation of the gradient information. A suitable prior for the desired image structures is learned as part of the training. The resulting network is trained and tested on a set of segmented vessels from lung CT scans and then applied to in-vivo photoacoustic measurement data