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We propose the deep Gauss-Newton (DGN) algorithm. The DGN allows one to take into account the knowledge of the forward model in a deep neural network by unrolling a Gauss-Newton optimization method. No regularization or step size needs to be chosen; they are learned through convolutional neural networks. The proposed algorithm does not require an initial reconstruction and is able to retrieve simultaneously the phase and absorption from a single-distance diffraction pattern. The DGN method was applied to both simulated and experimental data and permitted large improvements of the reconstruction error and of the resolution compared with a state-of-the-art iterative method and another neural-network-based reconstruction algorithm.
RESUMEN
We propose a nonlinear primal-dual algorithm for the retrieval of phase shift and absorption from a single x ray in-line phase contrast, or Fresnel diffraction, image. The algorithm permits us to regularize phase and absorption separately. We demonstrate that taking into account the nonlinearity in the reconstruction improves reconstruction compared with linear methods. We also demonstrate that choosing different regularizers for absorption and phase can improve the reconstructions. The use of the total variation and its generalization in a primal-dual approach allows us to exploit the sparsity of the investigated sample. On both simulated and real datasets, the proposed nonlinear primal-dual hybrid gradient (NL-PDHG) method yields reconstructions with considerably fewer artifacts and improved the normalized mean squared error compared with its linearized version.
RESUMEN
X-ray in-line phase contrast imaging relies on the measurement of Fresnel diffraction intensity patterns due to the phase shift and the attenuation induced by the object. The recovery of phase and attenuation from one or several diffraction patterns is a nonlinear ill-posed inverse problem. In this work, we propose supervised learning approaches using mixed scale dense (MS-D) convolutional neural networks to simultaneously retrieve the phase and the attenuation from x-ray phase contrast images. This network architecture uses dilated convolutions to capture features at different image scales and densely connects all feature maps. The long range information in images becomes quickly available, and greater receptive field size can be obtained without losing resolution. This network architecture seems to account for the effect of the Fresnel operator very efficiently. We train the networks using simulated data of objects consisting of either homogeneous components, characterized by a fixed ratio of the induced refractive phase shifts and attenuation, or heterogeneous components, consisting of various materials. We also train the networks in the image domain by applying a simple initial reconstruction using the adjoint of the Fréchet derivative. We compare the results obtained with the MS-D network to reconstructions using U-Net, another popular network architecture, as well as to reconstructions using the contrast transfer function method, a direct phase and attenuation retrieval method based on linearization of the direct problem. The networks are evaluated using simulated noisy data as well as images acquired at NanoMAX (MAX IV, Lund, Sweden). In all cases, large improvements of the reconstruction errors are obtained on simulated data compared to the linearized method. Moreover, on experimental data, the networks improve the reconstruction quantitatively, improving the low-frequency behavior and the resolution.
RESUMEN
X-ray propagation-based imaging techniques are well established at synchrotron radiation and laboratory sources. However, most reconstruction algorithms for such image modalities, also known as phase-retrieval algorithms, have been developed specifically for one instrument by and for experts, making the development and diffusion of such techniques difficult. Here, PyPhase, a free and open-source package for propagation-based near-field phase reconstructions, which is distributed under the CeCILL license, is presented. PyPhase implements some of the most popular phase-retrieval algorithms in a highly modular framework supporting its deployment on large-scale computing facilities. This makes the integration, the development of new phase-retrieval algorithms, and the deployment on different computing infrastructures straightforward. Its capabilities and simplicity are presented by application to data acquired at the synchrotron source MAX IV (Lund, Sweden).
