We consider here the problem of reconstructing an image from a few linear measurements. This problem has many biomedical applications, such as computerized tomography, magnetic resonance imaging and optical microscopy. While this problem has long been solved by compressed sensing methods, these are now outperformed by deeplearning approaches. However, understanding why a given network architecture works well is still an open question. In this study, we proposed to interpret the reconstruction problem as a Bayesian completion problem where the missing measurements are estimated from those acquired. From this point of view, a network emerges that includes a fully connected layer that provides the best linear completion scheme. This network has a lot fewer parameters to learn than direct networks, and it trains more rapidly than image-domain networks that correct pseudo inverse solutions. Although, this study focuses on computational optics, it might provide some insight for inverse problems that have similar formulations.
Single-pixel imaging allows low cost cameras to be built for imaging modalities where a conventional camera would either be too expensive or too cumbersome. This is very attractive for biomedical imaging applications based on hyperspectral measurements, such as image-guided surgery, which requires the full spectrum of fluorescence. A single-pixel camera essentially measures the inner product of the scene and a set of patterns. An inverse problem has to be solved to recover the original image from the raw measurement. The challenge in single-pixel imaging is to reconstruct the video sequence in real time from under-sampled data. Previous approaches have focused on the reconstruction of each frame independently, which fails to exploit the natural temporal redundancy in a video sequence. In this study, we propose a fast deep-learning reconstructor that exploits the spatio-temporal features in a video. In particular, we consider convolutional gated recurrent units that have low memory requirements. Our simulation shows than the proposed recurrent network improves the reconstruction quality compared to static approaches that reconstruct the video frames independently.
Single-pixel cameras that measure image coefficients have various promising applications, in particular for hyper-spectral imaging. Here, we investigate deep neural networks that when fed with experimental data can output high-quality images in real time. Assuming that the measurements are corrupted by mixed Poisson-Gaussian noise, we propose to map the raw data from the measurement domain to the image domain based on a Tikhonov regularization. This step can be implemented as the first layer of a deep neural network, followed by any architecture of layers that acts in the image domain. We also describe a framework for training the network in the presence of noise. In particular, our approach includes an estimation of the image intensity and experimental parameters, together with a normalization scheme that allows varying noise levels to be handled during training and testing. Finally, we present results from simulations and experimental acquisitions with varying noise levels. Our approach yields images with improved peak signal-to-noise ratios, even for noise levels that were foreseen during the training of the networks, which makes the approach particularly suitable to deal with experimental data. Furthermore, while this approach focuses on single-pixel imaging, it can be adapted for other computational optics problems.
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