A Deep Residual Neural Network for Image Reconstruction in Biomedical 3D Magnetic Induction Tomography

In recent years, it has become increasingly popular to solve inverse problems of various tomography methods with deep learning techniques. Here, a deep residual neural network (ResNet) is introduced to reconstruct the conductivity distribution of a biomedical, voluminous body in magnetic induction tomography (MIT). MIT is a relatively new, contactless and noninvasive tomography method. However, the ill-conditioned inverse problem of MIT is challenging to solve, especially for voluminous bodies with conductivities in the range of biological tissue. The proposed ResNet can reconstruct up to two cuboid perturbation objects with conductivities of 0.0 and 1.0 S/m in the whole voluminous body, even in the difficult-to-detect centre. The dataset used for training and testing contained simulated signals of cuboid perturbation objects with randomised lengths and positions. Furthermore, special care went into avoiding the inverse crime while creating the dataset. The calculated metrics showed good results over the test dataset, with an average correlation coefficient of 0.87 and mean squared error of 0.001. Robustness was tested on three special test cases containing unknown shapes, conductivities and a real measurement that showed error results well within the margin of the metrics of the test dataset. This indicates that a good approximation of the inverse function in MIT for up to two perturbation objects was achieved and the inverse crime was avoided.

Unsupervised knowledge-transfer for learned image reconstruction

Deep learning-based image reconstruction approaches have demonstrated impressive empirical performance in many imaging modalities. These approaches usually require a large amount of high-quality paired training data, which is often not available in medical imaging. To circumvent this issue we develop a novel unsupervised knowledge-transfer paradigm for learned reconstruction within a Bayesian framework. The proposed approach learns a reconstruction network in two phases. The first phase trains a reconstruction network with a set of ordered pairs comprising of ground truth images of ellipses and the corresponding simulated measurement data. The second phase fine-tunes the pretrained network to more realistic measurement data without supervision. By construction, the framework is capable of delivering predictive uncertainty information over the reconstructed image. We present extensive experimental results on low-dose and sparse-view computed tomography showing that the approach is competitive with several state-of-the-art supervised and unsupervised reconstruction techniques. Moreover, for test data distributed differently from the training data, the proposed framework can significantly improve reconstruction quality not only visually, but also quantitatively in terms of PSNR and SSIM, when compared with learned methods trained on the synthetic dataset only.

Self-Training Strategy Based on Finite Element Method for Adaptive Bioluminescence Tomography Reconstruction

Bioluminescence tomography (BLT) is a promising pre-clinical imaging technique for a wide variety of biomedical applications, which can non-invasively reveal functional activities inside living animal bodies through the detection of visible or near-infrared light produced by bioluminescent reactions. Recently, reconstruction approaches based on deep learning have shown great potential in optical tomography modalities. However, these reports only generate data with stationary patterns of constant target number, shape, and size. The neural networks trained by these data sets are difficult to reconstruct the patterns outside the data sets. This will tremendously restrict the applications of deep learning in optical tomography reconstruction. To address this problem, a self-training strategy is proposed for BLT reconstruction in this paper. The proposed strategy can fast generate large-scale BLT data sets with random target numbers, shapes, and sizes through an algorithm named random seed growth algorithm and the neural network is automatically self-trained. In addition, the proposed strategy uses the neural network to build a map between photon densities on surface and inside the imaged object rather than an end-to-end neural network that directly infers the distribution of sources from the photon density on surface. The map of photon density is further converted into the distribution of sources through the multiplication with stiffness matrix. Simulation, phantom, and mouse studies are carried out. Results show the availability of the proposed self-training strategy.

Deformation-Compensated Learning for Image Reconstruction Without Ground Truth

Deep neural networks for medical image reconstruction are traditionally trained using high-quality ground-truth images as training targets. Recent work on Noise2Noise (N2N) has shown the potential of using multiple noisy measurements of the same object as an alternative to having a ground-truth. However, existing N2N-based methods are not suitable for learning from the measurements of an object undergoing nonrigid deformation. This paper addresses this issue by proposing the deformation-compensated learning (DeCoLearn) method for training deep reconstruction networks by compensating for object deformations. A key component of DeCoLearn is a deep registration module, which is jointly trained with the deep reconstruction network without any ground-truth supervision. We validate DeCoLearn on both simulated and experimentally collected magnetic resonance imaging (MRI) data and show that it significantly improves imaging quality.

Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery

To solve inverse problems, plug-and-play (PnP) methods replace the proximal step in a convex optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network (DNN). Although such methods yield accurate solutions, they can be improved. For example, denoisers are usually designed/trained to remove white Gaussian noise, but the denoiser input error in PnP algorithms is usually far from white or Gaussian. Approximate message passing (AMP) methods provide white and Gaussian denoiser input error, but only when the forward operator is sufficiently random. In this work, for Fourier-based forward operators, we propose a PnP algorithm based on generalized expectation-consistent (GEC) approximation-a close cousin of AMP-that offers predictable error statistics at each iteration, as well as a new DNN denoiser that leverages those statistics. We apply our approach to magnetic resonance (MR) image recovery and demonstrate its advantages over existing PnP and AMP methods.

Monte Carlo simulation of sensitivity functions for few-view computed tomography of strongly absorbing media

The paper describes a sensitivity function calculation method for few-view X-ray computed tomography of strongly absorbing objects. It is based on a probabilistic interpretation of energy transport through the object from a source to a detector. A PRIZMA code package is used to track photons. The code is developed at FSUE “RFNC–VNIITF named after Academ. E. I. Zababakhin” and implements a stochastic Monte Carlo method. The value of the sensitivity function in a discrete cell of the reconstruction region is assumed to be directly proportional to the fraction of photon trajectories which cross the cell from all those recorded by the detector. The method’s efficiency is validated through a numerical experiment on the reconstruction of a section of a spherical heavy-metal phantom with an air cavity and a density difference of 25 Ṫhe proposed method is shown to outperform the method based on projection approximation in case of reconstruction from 9 views.

Physics-enhanced neural network for phase retrieval from two diffraction patterns

In this work, we propose a physics-enhanced two-to-one Y-neural network (two inputs and one output) for phase retrieval of complex wavefronts from two diffraction patterns. The learnable parameters of the Y-net are optimized by minimizing a hybrid loss function, which evaluates the root-mean-square error and normalized Pearson correlated coefficient on the two diffraction planes. An angular spectrum method network is designed for self-supervised training on the Y-net. Amplitudes and phases of wavefronts diffracted by a USAF-1951 resolution target, a phase grating of 200 lp/mm, and a skeletal muscle cell were retrieved using a Y-net with 100 learning iterations. Fast reconstructions could be realized without constraints or a priori knowledge of the samples.

A Complex-Valued Self-Supervised Learning-Based Method for Specific Emitter Identification

Specific emitter identification (SEI) refers to distinguishing emitters using individual features extracted from wireless signals. The current SEI methods have proven to be accurate in tackling large labeled data sets at a high signal-to-noise ratio (SNR). However, their performance declines dramatically in the presence of small samples and a significant noise environment. To address this issue, we propose a complex self-supervised learning scheme to fully exploit the unlabeled samples, comprised of a pretext task adopting the contrastive learning concept and a downstream task. In the former task, we design an optimized data augmentation method based on communication signals to serve the contrastive conception. Then, we embed a complex-valued network in the learning to improve the robustness to noise. The proposed scheme demonstrates the generality of handling the small and sufficient samples cases across a wide range from 10 to 400 being labeled in each group. The experiment also shows a promising accuracy and robustness where the recognition results increase at 10–16% from 10–15 SNR.

The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem

Instability is the Achilles’ heel of modern artificial intelligence (AI) and a paradox, with training algorithms finding unstable neural networks (NNs) despite the existence of stable ones. This foundational issue relates to Smale’s 18th mathematical problem for the 21st century on the limits of AI. By expanding methodologies initiated by Gödel and Turing, we demonstrate limitations on the existence of (even randomized) algorithms for computing NNs. Despite numerous existence results of NNs with great approximation properties, only in specific cases do there also exist algorithms that can compute them. We initiate a classification theory on which NNs can be trained and introduce NNs that—under suitable conditions—are robust to perturbations and exponentially accurate in the number of hidden layers.

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence of stable neural networks (NNs). We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities; however, there does not exist any algorithm, even randomized, that can train (or compute) such a NN. For any positive integers K>2 and L, there are cases where simultaneously 1) no randomized training algorithm can compute a NN correct to K digits with probability greater than 1/2; 2) there exists a deterministic training algorithm that computes a NN with K –1 correct digits, but any such (even randomized) algorithm needs arbitrarily many training data; and 3) there exists a deterministic training algorithm that computes a NN with K –2 correct digits using no more than L training samples. These results imply a classification theory describing conditions under which (stable) NNs with a given accuracy can be computed by an algorithm. We begin this theory by establishing sufficient conditions for the existence of algorithms that compute stable NNs in inverse problems. We introduce fast iterative restarted networks (FIRENETs), which we both prove and numerically verify are stable. Moreover, we prove that only O(|log (ϵ)|) layers are needed for an ϵ-accurate solution to the inverse problem.

Solving Inverse Electrocardiographic Mapping Using Machine Learning and Deep Learning Frameworks

Electrocardiographic imaging (ECGi) reconstructs electrograms at the heart's surface using the potentials recorded at the body's surface. This is called the inverse problem of electrocardiography. This study aimed to improve on the current solution methods using machine learning and deep learning frameworks. Electrocardiograms were simultaneously recorded from pigs' ventricles and their body surfaces. The Fully Connected Neural network (FCN), Long Short-term Memory (LSTM), Convolutional Neural Network (CNN) methods were used for constructing the model. A method is developed to align the data across different pigs. We evaluated the method using leave-one-out cross-validation. For the best result, the overall median of the correlation coefficient of the predicted ECG wave was 0.74. This study demonstrated that a neural network can be used to solve the inverse problem of ECGi with relatively small datasets, with an accuracy compatible with current standard methods.

Physics-based learning with channel attention for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a computational imaging technology for large field-of-view, high resolution and quantitative phase imaging. In FPM, low-resolution intensity images captured with angle-varying illumination are synthesized in Fourier space with phase retrieval approaches. However, system errors such as pupil aberration and light-emitting diode (LED) intensity error seriously affect the reconstruction performance. In this article, we propose a physics-based neural network with channel attention for FPM reconstruction. With the channel attention module, which is introduced into physics-based neural networks for the first time, the spatial distribution of LED intensity can be adaptively corrected. Besides, the channel attention module is used to synthesize different Zernike modes and recover the pupil function. Detailed simulations and experiments are carried out to validate the effectiveness and robustness of the proposed method. The results demonstrate that our method achieves better performance in high-resolution complex field reconstruction, LED intensity correction and pupil function recovery compared with the state-of-art methods. The combination with deep neural network structures like channel attention modules significantly enhance the performance of physics-based neural networks and will promote the application of FPM in practical use.

Computing a projection operator onto the null space of a linear imaging operator: tutorial

Many imaging systems can be approximately described by a linear operator that maps an object property to a collection of discrete measurements. However, even in the absence of measurement noise, such operators are generally "blind" to certain components of the object, and hence information is lost in the imaging process. Mathematically, this is explained by the fact that the imaging operator can possess a null space. All objects in the null space, by definition, are mapped to a collection of identically zero measurements and are hence invisible to the imaging system. As such, characterizing the null space of an imaging operator is of fundamental importance when comparing and/or designing imaging systems. A characterization of the null space can also facilitate the design of regularization strategies for image reconstruction methods. Characterizing the null space via an associated projection operator is, in general, a computationally demanding task. In this tutorial, computational procedures for establishing projection operators that map an object to the null space of a discrete-to-discrete imaging operator are surveyed. A new machine-learning-based approach that employs a linear autoencoder is also presented. The procedures are demonstrated by use of biomedical imaging examples, and their computational complexities and memory requirements are compared.

Block-based spectral image reconstruction for compressive spectral imaging using smoothness on graphs

A novel reconstruction method for compressive spectral imaging is designed by assuming that the spectral image of interest is sufficiently smooth on a collection of graphs. Since the graphs are not known in advance, we propose to infer them from a panchromatic image using a state-of-the-art graph learning method. Our approach leads to solutions with closed-form that can be found efficiently by solving multiple sparse systems of linear equations in parallel. Extensive simulations and an experimental demonstration show the merits of our method in comparison with traditional methods based on sparsity and total variation and more recent methods based on low-rank minimization and deep-based plug-and-play priors. Our approach may be instrumental in designing efficient methods based on deep neural networks and covariance estimation.

Self-supervised IVIM DWI parameter estimation with a physics based forward model

PURPOSE

To assess the robustness and repeatability of intravoxel incoherent motion model (IVIM) parameter estimation for the diffusion-weighted MRI in the abdominal organs under the constraints of noisy diffusion signal using a novel neural network method.

METHODS

Clinically acquired abdominal scans of Crohn's disease patients were retrospectively analyzed with regions segmented in the kidney cortex, spleen, liver, and bowel. A novel IVIM parameter fitting method based on the principle of a physics guided self-supervised convolutional neural network that does not require reference parameter estimates for training was compared to a conventional non-linear least squares (NNLS) algorithm, and a voxelwise trained artificial neural network (ANN).

RESULTS

Results showed substantial increase in parameter robustness to the noise corrupted signal. In an intra-session repeatability experiment, the proposed method showed reduced coefficient of variation (CoV) over multiple acquisitions in comparison to conventional NLLS method and comparable performance to ANN. The use of D and f estimates from the proposed method led to the smallest misclassification error in linear discriminant analysis for characterization between normal and abnormal Crohn's disease bowel tissue. The fitting of D∗ parameter remains to be challenging.

CONCLUSION

The proposed method yields robust estimates of D and f IVIM parameters under the constraints of noisy diffusion signal. This indicates a potential for the use of the proposed method in conjunction with accelerated DW-MRI acquisition strategies, which would typically result in lower signal to noise ratio.

Report on the AAPM deep-learning sparse-view CT (DL-sparse-view CT) Grand Challenge

PURPOSE

The purpose of the challenge is to find the deep-learning technique for sparse-view CT image reconstruction that can yield the minimum RMSE under ideal conditions, thereby addressing the question of whether or not deep learning can solve inverse problems in imaging.

METHODS

The challenge set-up involves a 2D breast CT simulation, where the simulated breast phantom has random fibro-glandular structure and high-contrast specks. The phantom allows for arbitrarily large training sets to be generated with perfectly known truth. The training set consists of 4000 cases where each case consists of the truth image, 128-view sinogram data, and the corresponding 128-view filtered back-projection (FBP) image. The networks are trained to predict the truth image from either the sinogram or FBP data. Geometry information is not provided. The participating algorithms are tested on a data set consisting of 100 new cases.

RESULTS

About 60 groups participated in the challenge at the validation phase, and 25 groups submitted test-phase results along with reports on their deep-learning methodology. The winning team improved reconstruction accuracy by two orders of magnitude over our previous CNN-based study on a similar test problem.

CONCLUSIONS

The DL-sparse-view challenge provides a unique opportunity to examine the state-of-the-art in deep-learning techniques for solving the sparse-view CT inverse problem. This article is protected by copyright. All rights reserved.

Inpainted Image Reconstruction Using an Extended Hopfield Neural Network Based Machine Learning System

This paper considers the use of a machine learning system for the reconstruction and recognition of distorted or damaged patterns, in particular, images of faces partially covered with masks. The most up-to-date image reconstruction structures are based on constrained optimization algorithms and suitable regularizers. In contrast with the above-mentioned image processing methods, the machine learning system presented in this paper employs the superposition of system vectors setting up asymptotic centers of attraction. The structure of the system is implemented using Hopfield-type neural network-based biorthogonal transformations. The reconstruction property gives rise to a superposition processor and reversible computations. Moreover, this paper's distorted image reconstruction sets up associative memories where images stored in memory are retrieved by distorted/inpainted key images.

Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems

Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond to the likelihood and prior-probability models, respectively. The Bayesian approach gives more flexibility in choosing these terms and, in particular, the prior term via hierarchical models and hidden variables. However, the Bayesian computations can become very heavy computationally. The machine learning (ML) methods such as classification, clustering, segmentation, and regression, based on neural networks (NN) and particularly convolutional NN, deep NN, physics-informed neural networks, etc. can become helpful to obtain approximate practical solutions to inverse problems. In this tutorial article, particular examples of image denoising, image restoration, and computed-tomography (CT) image reconstruction will illustrate this cooperation between ML and inversion.

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has good generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

Scan-free end-to-end new approach for snapshot camera spectral sensitivity estimation

Spectral sensitivity is largely related to sensor imaging, which has drawn widespread attention in computer vision. Accurate estimation becomes increasingly urgent because manufacturers rarely disclose it. In this Letter, we present a novel, compact, inexpensive, and real-time computational system for snapshot spectral sensitivity estimation. A multi-scale camera based on the multi-scale convolutional neural network is first proposed, to the best of our knowledge, to automatically extract multiplexing features of an input image by multiscale deep learning, which is vital to solving the inverse problem in sensitivity estimation. Our network is flexible and can be designed with different convolutional kernel sizes for a given application. We build a dataset with 10,500 raw images and generate an excellent pre-trained model. Commercial cameras are adopted to test model validity; the results show that our system can achieve estimation accuracy as high as 91.35%. We provide a method for system design, propose a deep learning network, build a dataset, demonstrate training process, and present experimental results with high precision. This simple and effective method provides an accurate approach for precise estimation of spectral sensitivity and is suitable for computational applications such as pathological digital stain, virtual/augmented reality display, and high-quality image acquisition.

A framework for automated structure elucidation from routine NMR spectra

Methods to automate structure elucidation that can be applied broadly across chemical structure space have the potential to greatly accelerate chemical discovery. NMR spectroscopy is the most widely used and arguably the most powerful method for elucidating structures of organic molecules. Here we introduce a machine learning (ML) framework that provides a quantitative probabilistic ranking of the most likely structural connectivity of an unknown compound when given routine, experimental one dimensional ¹H and/or ¹³C NMR spectra. In particular, our ML-based algorithm takes input NMR spectra and (i) predicts the presence of specific substructures out of hundreds of substructures it has learned to identify; (ii) annotates the spectrum to label peaks with predicted substructures; and (iii) uses the substructures to construct candidate constitutional isomers and assign to them a probabilistic ranking. Using experimental spectra and molecular formulae for molecules containing up to 10 non-hydrogen atoms, the correct constitutional isomer was the highest-ranking prediction made by our model in 67.4% of the cases and one of the top-ten predictions in 95.8% of the cases. This advance will aid in solving the structure of unknown compounds, and thus further the development of automated structure elucidation tools that could enable the creation of fully autonomous reaction discovery platforms.

A machine learning model and graph generator were able to accurately predict for the presence of nearly 1000 substructures and the connectivity of small organic molecules from experimental 1D NMR data.

On Architecture Selection for Linear Inverse Problems with Untrained Neural Networks

In recent years, neural network based image priors have been shown to be highly effective for linear inverse problems, often significantly outperforming conventional methods that are based on sparsity and related notions. While pre-trained generative models are perhaps the most common, it has additionally been shown that even untrained neural networks can serve as excellent priors in various imaging applications. In this paper, we seek to broaden the applicability and understanding of untrained neural network priors by investigating the interaction between architecture selection, measurement models (e.g., inpainting vs. denoising vs. compressive sensing), and signal types (e.g., smooth vs. erratic). We motivate the problem via statistical learning theory, and provide two practical algorithms for tuning architectural hyperparameters. Using experimental evaluations, we demonstrate that the optimal hyperparameters may vary significantly between tasks and can exhibit large performance gaps when tuned for the wrong task. In addition, we investigate which hyperparameters tend to be more important, and which are robust to deviations from the optimum.

Unified Supervised-Unsupervised (SUPER) Learning for X-Ray CT Image Reconstruction

Traditional model-based image reconstruction (MBIR) methods combine forward and noise models with simple object priors. Recent machine learning methods for image reconstruction typically involve supervised learning or unsupervised learning, both of which have their advantages and disadvantages. In this work, we propose a unified supervised-unsupervised (SUPER) learning framework for X-ray computed tomography (CT) image reconstruction. The proposed learning formulation combines both unsupervised learning-based priors (or even simple analytical priors) together with (supervised) deep network-based priors in a unified MBIR framework based on a fixed point iteration analysis. The proposed training algorithm is also an approximate scheme for a bilevel supervised training optimization problem, wherein the network-based regularizer in the lower-level MBIR problem is optimized using an upper-level reconstruction loss. The training problem is optimized by alternating between updating the network weights and iteratively updating the reconstructions based on those weights. We demonstrate the learned SUPER models' efficacy for low-dose CT image reconstruction, for which we use the NIH AAPM Mayo Clinic Low Dose CT Grand Challenge dataset for training and testing. In our experiments, we studied different combinations of supervised deep network priors and unsupervised learning-based or analytical priors. Both numerical and visual results show the superiority of the proposed unified SUPER methods over standalone supervised learning-based methods, iterative MBIR methods, and variations of SUPER obtained via ablation studies. We also show that the proposed algorithm converges rapidly in practice.

Conditional Variational Autoencoder for Learned Image Reconstruction

Learned image reconstruction techniques using deep neural networks have recently gained popularity and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect information uncertainty. In this work, we develop a novel computational framework that approximates the posterior distribution of the unknown image at each query observation. The proposed framework is very flexible: it handles implicit noise models and priors, it incorporates the data formation process (i.e., the forward operator), and the learned reconstructive properties are transferable between different datasets. Once the network is trained using the conditional variational autoencoder loss, it provides a computationally efficient sampler for the approximate posterior distribution via feed-forward propagation, and the summarizing statistics of the generated samples are used for both point-estimation and uncertainty quantification. We illustrate the proposed framework with extensive numerical experiments on positron emission tomography (with both moderate and low-count levels) showing that the framework generates high-quality samples when compared with state-of-the-art methods.

Differentiable model-based adaptive optics for two-photon microscopy

Aberrations limit scanning fluorescence microscopy when imaging in scattering materials such as biological tissue. Model-based approaches for adaptive optics take advantage of a computational model of the optical setup. Such models can be combined with the optimization techniques of machine learning frameworks to find aberration corrections, as was demonstrated for focusing a laser beam through aberrations onto a camera [Opt. Express2826436 (26436)10.1364/OE.403487]. Here, we extend this approach to two-photon scanning microscopy. The developed sensorless technique finds corrections for aberrations in scattering samples and will be useful for a range of imaging application, for example in brain tissue.

Learning Optimal Wavefront Shaping for Multi-Channel Imaging

Fast acquisition of depth information is crucial for accurate 3D tracking of moving objects. Snapshot depth sensing can be achieved by wavefront coding, in which the point-spread function (PSF) is engineered to vary distinctively with scene depth by altering the detection optics. In low-light applications, such as 3D localization microscopy, the prevailing approach is to condense signal photons into a single imaging channel with phase-only wavefront modulation to achieve a high pixel-wise signal to noise ratio. Here we show that this paradigm is generally suboptimal and can be significantly improved upon by employing multi-channel wavefront coding, even in low-light applications. We demonstrate our multi-channel optimization scheme on 3D localization microscopy in densely labelled live cells where detectability is limited by overlap of modulated PSFs. At extreme densities, we show that a split-signal system, with end-to-end learned phase masks, doubles the detection rate and reaches improved precision compared to the current state-of-the-art, single-channel design. We implement our method using a bifurcated optical system, experimentally validating our approach by snapshot volumetric imaging and 3D tracking of fluorescently labelled subcellular elements in dense environments.

An end-to-end-trainable iterative network architecture for accelerated radial multi-coil 2D cine MR image reconstruction

PURPOSE

Iterative convolutional neural networks (CNNs) which resemble unrolled learned iterative schemes have shown to consistently deliver state-of-the-art results for image reconstruction problems across different imaging modalities. However, because these methods include the forward model in the architecture, their applicability is often restricted to either relatively small reconstruction problems or to problems with operators which are computationally cheap to compute. As a consequence, they have not been applied to dynamic non-Cartesian multi-coil reconstruction problems so far.

METHODS

In this work, we propose a CNN architecture for image reconstruction of accelerated 2D radial cine MRI with multiple receiver coils. The network is based on a computationally light CNN component and a subsequent conjugate gradient (CG) method which can be jointly trained end-to-end using an efficient training strategy. We investigate the proposed training strategy and compare our method with other well-known reconstruction techniques with learned and non-learned regularization methods.

RESULTS

Our proposed method outperforms all other methods based on non-learned regularization. Further, it performs similar or better than a CNN-based method employing a 3D U-Net and a method using adaptive dictionary learning. In addition, we empirically demonstrate that even by training the network with only iteration, it is possible to increase the length of the network at test time and further improve the results.

CONCLUSIONS

End-to-end training allows to highly reduce the number of trainable parameters of and stabilize the reconstruction network. Further, because it is possible to change the length of the network at the test time, the need to find a compromise between the complexity of the CNN-block and the number of iterations in each CG-block becomes irrelevant.

Review of deep learning for photoacoustic imaging

Machine learning has been developed dramatically and witnessed a lot of applications in various fields over the past few years. This boom originated in 2009, when a new model emerged, that is, the deep artificial neural network, which began to surpass other established mature models on some important benchmarks. Later, it was widely used in academia and industry. Ranging from image analysis to natural language processing, it fully exerted its magic and now become the state-of-the-art machine learning models. Deep neural networks have great potential in medical imaging technology, medical data analysis, medical diagnosis and other healthcare issues, and is promoted in both pre-clinical and even clinical stages. In this review, we performed an overview of some new developments and challenges in the application of machine learning to medical image analysis, with a special focus on deep learning in photoacoustic imaging. The aim of this review is threefold: (i) introducing deep learning with some important basics, (ii) reviewing recent works that apply deep learning in the entire ecological chain of photoacoustic imaging, from image reconstruction to disease diagnosis, (iii) providing some open source materials and other resources for researchers interested in applying deep learning to photoacoustic imaging.

Rapid reconstruction of highly undersampled, non-Cartesian real-time cine k-space data using a perceptual complex neural network (PCNN)

Highly accelerated real-time cine MRI using compressed sensing (CS) is a promising approach to achieve high spatio-temporal resolution and clinically acceptable image quality in patients with arrhythmia and/or dyspnea. However, its lengthy image reconstruction time may hinder its clinical translation. The purpose of this study was to develop a neural network for reconstruction of non-Cartesian real-time cine MRI k-space data faster (<1 min per slice with 80 frames) than graphics processing unit (GPU)-accelerated CS reconstruction, without significant loss in image quality or accuracy in left ventricular (LV) functional parameters. We introduce a perceptual complex neural network (PCNN) that trains on complex-valued MRI signal and incorporates a perceptual loss term to suppress incoherent image details. This PCNN was trained and tested with multi-slice, multi-phase, cine images from 40 patients (20 for training, 20 for testing), where the zero-filled images were used as input and the corresponding CS reconstructed images were used as practical ground truth. The resulting images were compared using quantitative metrics (structural similarity index (SSIM) and normalized root mean square error (NRMSE)) and visual scores (conspicuity, temporal fidelity, artifacts, and noise scores), individually graded on a five-point scale (1, worst; 3, acceptable; 5, best), and LV ejection fraction (LVEF). The mean processing time per slice with 80 frames for PCNN was 23.7 ± 1.9 s for pre-processing (Step 1, same as CS) and 0.822 ± 0.004 s for dealiasing (Step 2, 166 times faster than CS). Our PCNN produced higher data fidelity metrics (SSIM = 0.88 ± 0.02, NRMSE = 0.014 ± 0.004) compared with CS. While all the visual scores were significantly different (P < 0.05), the median scores were all 4.0 or higher for both CS and PCNN. LVEFs measured from CS and PCNN were strongly correlated (R² = 0.92) and in good agreement (mean difference = -1.4% [2.3% of mean]; limit of agreement = 10.6% [17.6% of mean]). The proposed PCNN is capable of rapid reconstruction (25 s per slice with 80 frames) of non-Cartesian real-time cine MRI k-space data, without significant loss in image quality or accuracy in LV functional parameters.

On the value of CTIS imagery for neural-network-based classification: a simulation perspective

The computed tomography imaging spectrometer (CTIS) is a snapshot hyperspectral imaging system. Its output is a 2D image of multiplexed spatiospectral projections of the hyperspectral cube of the scene. Traditionally, the 3D cube is reconstructed from this image before further analysis. In this paper, we show that it is possible to learn information directly from the CTIS raw output, by training a neural network to perform binary classification on such images. The use case we study is an agricultural one, as snapshot imagery is used substantially in this field: the detection of apple scab lesions on leaves. To train the network appropriately and to study several degrees of scab infection, we simulated CTIS images of scabbed leaves. This was made possible with a novel CTIS simulator, where special care was taken to preserve realistic pixel intensities compared to true images. To the best of our knowledge, this is the first application of compressed learning on a simulated CTIS system.