Fourier ptychographic microscopy with untrained deep neural network priors.

Fourier ptychographic microscopy (FPM) is a newly developed microscopic technique for large field of view, high-resolution and quantitative phase imaging by combining the techniques from ptychographic imaging, aperture synthesizing and phase retrieval. In FPM, an LED array is utilized to illuminate the specimen from different angles and the corresponding intensity images are synthesized to reconstruct a high-resolution complex field. As a flexible and low-cost approach to achieve high-resolution, wide-field and quantitative phase imaging, FPM is of enormous potential in biomedical applications such as hematology and pathology. Conventionally, the FPM reconstruction problem is solved by using a phase retrieval method, termed Alternate Projection. By iteratively updating the Fourier spectrum with low-resolution-intensity images, the result converges to a high-resolution complex field. Here we propose a new FPM reconstruction framework with deep learning methods and design a multiscale, deep residual neural network for FPM reconstruction. We employ the widely used open-source deep learning library PyTorch to train and test our model and carefully choose the hyperparameters of our model. To train and analyze our model, we build a large-scale simulation dataset with an FPM imaging model and an actual dataset captured with an FPM system. The simulation dataset and actual dataset are separated as training datasets and test datasets, respectively. Our model is trained with the simulation training dataset and fine tuned with the fine-tune dataset, which contains actual training data. Both our model and the conventional method are tested on the simulation test dataset and the actual test dataset to evaluate the performances. We also show the reconstruction result of another neural network-based method for comparison. The experiments demonstrate that our model achieves better reconstruction results and consumes much less time than conventional methods. The results also point out that our model is more robust under system aberrations such as noise and blurring (fewer intensity images) compared with conventional methods.

Deep neural network (DNN) models, particularly convolutional neural networks (CNNs), have demonstrated remarkable performance in biomedical image classification due to their ability to automatically learn features from large datasets. One common challenge in the preparation of large, microscopic datasets for DNN tasks is sample defocusing, potentially impairing the model performance. To handle defocusing, computational imaging, or specifically quantitative phase imaging (QPI), performs digital refocusing by using both the phase and the amplitude of the complex optical field. This leads us to investigate whether feeding the complex field into DNN would potentially address the defocusing problem as in-focus information is implicitly encoded in the complex field. In this paper, we assess the feasibility of employing neural networks to directly process full amplitude and phase data from a defocus plane without digital refocusing. Our specific focus lies in understanding the tolerance for defocus in image classification neural networks when amplitude and phase are taken as inputs. To accomplish this, we used Fourier ptychography microscopy (FPM) to acquire in-focus phase and amplitude images of two distinct object types - normal red blood cells and echinocytes. We then digitally propagate the complex field to generate progressively defocused images of the samples to serve as training and testing datasets for image classification neural networks. While the digitally defocused images contain sufficient information to recover the original in-focus images, we observed that current standard implementations of deep learning models are unable to effectively utilize the defocused field to distinguish between the two cell types. We conclude that the physical-model-based digital refocusing capability of QPI remains indispensable for overcoming defocusing issues in current standard DNN models.

High-throughput quantitative phase imaging (QPI) is essential to cellular phenotypes characterization as it allows high-content cell analysis and avoids adverse effects of staining reagents on cellular viability and cell signaling. Among different approaches, Fourier ptychographic microscopy (FPM) is probably the most promising technique to realize high-throughput QPI by synthesizing a wide-field, high-resolution complex image from multiple angle-variably illuminated, low-resolution images. However, the large dataset requirement in conventional FPM significantly limits its imaging speed, resulting in low temporal throughput. Moreover, the underlying theoretical mechanism as well as optimum illumination scheme for high-accuracy phase imaging in FPM remains unclear. Herein, we report a high-speed FPM technique based on programmable annular illuminations (AIFPM). The optical-transfer-function (OTF) analysis of FPM reveals that the low-frequency phase information can only be correctly recovered if the LEDs are precisely located at the edge of the objective numerical aperture (NA) in the frequency space. By using only 4 low-resolution images corresponding to 4 tilted illuminations matching a 10×, 0.4 NA objective, we present the high-speed imaging results of in vitro Hela cells mitosis and apoptosis at a frame rate of 25 Hz with a full-pitch resolution of 655 nm at a wavelength of 525 nm (effective NA = 0.8) across a wide field-of-view (FOV) of 1.77 mm2, corresponding to a space–bandwidth–time product of 411 megapixels per second. Our work reveals an important capability of FPM towards high-speed high-throughput imaging of in vitro live cells, achieving video-rate QPI performance across a wide range of scales, both spatial and temporal.

The integration of neural network and physical reconstruction model for Fourier ptychographic microscopy

Adaptive denoising method for Fourier ptychographic microscopy

White blood cells (WBC) play a significant role in human immune system, so WBC detection is a meaningful work. In this paper, we propose a novel framework which combines Fourier ptychographic microscopy (FPM) and SO-you only look once (YOLO) for WCB detection. FPM is a recently developed microscope technology which can achieve high-resolution, wide-field, and quantitative phase imaging at the same time without mechanical moving and phase measurement. With the FPM, we can get high resolution, wide field-of-view blood cell images at one time. After obtaining high-resolution images, we propose SO-YOLO as our detection method. As a convolutional neural network, the SO-YOLO outperforms the state-of-the-art detection methods both in accuracy and speed. The proposed framework in this paper can be used in clinical diagnose, because the experiment setup is flexible and the detection is fast. The data set in this paper is made with FPM by ourselves. Our data set contains 1000 color high resolution images and all the WBC has been detected and counted by a human expert. The detection results by the experts are regarded as the ground truth. The experiment results show that the SO-YOLO performs well in detecting small objects compared with other methods.

In recent years, a lot of power allocation algorithms have been proposed to maximize spectral efficiency (SE) and energy efficiency (EE) for the distributed antenna systems (DAS). However, the traditional iterative power allocation algorithms are difficult to be implemented in reality because of their high computational complexity. With the development of machine learning algorithms, it has been proved that the machine learning method has excellent learning ability and low computational complexity, which can approximate the traditional iterative power allocation well and be easily to be implemented in reality. In this paper, we propose a new deep neural network (DNN) model for DAS. From the perspective of machine learning, traditional iterative algorithms can be regarded as a nonlinear mapping between user channel realizations and optimal power allocation schemes. Therefore, we train the DNN to learn the nonlinear mapping between the user channel realizations and the corresponding power allocation schemes based on the traditional iterative algorithm. Then, a power allocation schemes based on DNN method is developed to maximize SE and EE for DAS. The simulation results show that the proposed scheme can not only obtain the almost similar performance as the traditional iterative algorithm, but also reduce much online computational time.

Fourier ptychography microscopy(FPM) is a recently developed computational imaging approach for microscopic super-resolution imaging. By turning on each light-emitting-diode (LED) located on different position on the LED array sequentially and acquiring the corresponding images that contain different spatial frequency components, high spatial resolution and quantitative phase imaging can be achieved in the case of large field-of-view. Nevertheless, FPM has high requirements for the system construction and data acquisition processes, such as precise LEDs position, accurate focusing and appropriate exposure time, which brings many limitations to its practical applications. In this paper, inspired by artificial neural network, we propose a Fourier ptychography multi-parameter neural network (FPMN) with composite physical prior optimization. A hybrid parameter determination strategy combining physical imaging model and data-driven network training is proposed to recover the multi layers of the network corresponding to different physical parameters, including sample complex function, system pupil function, defocus distance, LED array position deviation and illumination intensity fluctuation, etc. Among these parameters, LED array position deviation is recovered based on the features of brightfield to darkfield transition low-resolution images while the others are recovered in the process of training of the neural network. The feasibility and effectiveness of FPMN are verified through simulations and actual experiments. Therefore FPMN can evidently reduce the requirement for practical applications of FPM.

Structural imaging using light microscopy is a cornerstone of histology and cytology. However, the utility of the optical microscope for diagnostic imaging is limited by the fundamental tradeoff between the field of view and spatial resolution and a reliance on exogenous dyes to generate sufficient image contrast. Fourier Ptychographic Microscopy (FPM) is a complex imaging modality with the potential to overcome these limitations by recovering high-resolution images of sample amplitude and phase from a set of low-resolution raw images captured under inclined illumination. In this article we explore the application of FPM to clinical imaging using a simple, low-cost FPM system and simulated and experimental data to explore the influence of both image acquisition parameters and hardware configuration on image quality and imaging throughput. The practical performance of the method is investigated by imaging peripheral blood films and histological tissue sections. We find that, at the cost of increased computational complexity, FPM increases the information capture capacity of the optical microscope significantly, allowing label-free examination and quantification of features such as tissue and cell morphology over large sample areas.

Fourier ptychographic microscopy (FPM) is an attractive method to extend the resolution beyond the conventional limit defined by a microscope optics, sharing properties with ptychographic, synthetic aperture imaging and phase retrieval. The algorithm uses a sequence of low-resolution (LR) images acquired under angularly varying illumination to reconstruct a high-resolution (HR) image. However, traditional FPM may trap to the sub-optimal solution, since brute-force replacement in the Fourier domain is applied. To address this problem, we propose here a weighted replacement for Fourier ptychographic microscopy (WFPM). We employ the weighted average of spectrums corresponding to different illumination angle to replace the overlapped regions in the Fourier domain. A series of experimental results demonstrate that the reconstructed image using the proposed WFPM shows a better quality and a faster convergence compared with the results obtained by FPM.

Deep learning has achieved noteworthy success in various applications. There is a new trend of adopting deep learning methods to study partial differential equations (PDEs). In this article, we use a kind of parallel deep neural networks (PDNNs) to approximate the solution of the Navier–Stokes equations coupled with the heat equation. The approach embeds the PDE formula into the loss function of the neural networks and the resulting networks is trained to meet the equations along with the boundary conditions. Moreover, the approximate ability of the PDNNs is demonstrated by the theoretical analysis of convergence. Finally, we present numerous numerical examples to verify effectiveness of the PDNNs, in which the viscosity is a constant, a function dependent on the space variable and a function of the temperature .

Automated image classification is an essential task of the computer vision field. The tagging of images into a set of predefined groups is referred to as image classification. The implementation of computer vision to automate image classification would be beneficial because manual image evaluation and identification can be time-consuming, particularly when there are many images of different classes. Deep learning approaches are proven to overperform existing machine learning techniques in many fields in recent years, and computer vision is one of the most notable examples. The very deep neural network (VDCNN) is a powerful deep learning model for image classification, and this paper examines it briefly using MNIST handwritten digit dataset. This dataset is used to prove the efficacy of very deep neural networks over other deep learning models. The proposed study aims to comprehend the very deep neural network architecture used to accomplish a handwritten digit recognition task. The feasibility of the proposed model is evaluated using mean accuracy, validation accuracy, and standard deviation. The study results of the very deep neural network model are compared to a convolutional neural network and convolutional neural network with batch normalization. According to the results of the comparison study, very deep neural networks achieve high accuracy of 99.1% for a handwritten dataset. The outcome of the proposed work is used to interpret how well a very deep neural network performs when compared to the other two models of deep neural networks. This proposed architecture may be used to automate the classification of handwritten digits dataset.

Summary A meticulous interpretation of steady-state or unsteady-state relative permeability (Kr) experimental data is required to determine a complete set of Kr curves. In this work, different machine learning (ML) models were developed to assist in a faster estimation of these curves from steady-state drainage coreflooding experimental runs. These ML algorithms include gradient boosting (GB), random forest (RF), extreme gradient boosting (XGB), and deep neural network (DNN) with a main focus on and comparison of the two latter algorithms (XGB and DNN). Based on existing mathematical models, a leading-edge framework was developed where a large database of Kr and capillary pressure (Pc) curves were generated. This database was used to perform thousands of coreflood simulation runs representing oil-water drainage steady-state experiments. The results obtained from these simulation runs, mainly pressure drop along with other conventional core analysis data, were used to estimate analytical Kr curves based on Darcy’s law. These analytically estimated Kr curves along with the previously generated Pc curves were fed as features into the ML model. The entire data set was split into 80% for training and 20% for testing. The k-fold cross-validation technique was applied to increase the model’s accuracy by splitting 80% of the training data into 10 folds. In this manner, for each of the 10 experiments, nine folds were used for training and the remaining fold was used for model validation. Once the model was trained and validated, it was subjected to blind testing on the remaining 20% of the data set. The ML model learns to capture fluid flow behavior inside the core from the training data set. In terms of applicability of these ML models, two sets of experimental data were needed as input; the first was the analytically estimated Kr curves from the steady-state drainage coreflooding experiments, while the other was the Pc curves estimated from centrifuge or mercury injection capillary pressure (MICP) measurements. The trained/tested model was then able to estimate Kr curves based on the experimental results fed as input. Furthermore, to test the performance of the ML model when only one set of experimental data is available to an end user, a recurrent neural network (RNN) algorithm was trained/tested to predict Kr curves in the absence of Pc curves as an input. The performance of the three developed models (XGB, DNN, and RNN) was assessed using the values of the coefficient of determination (R2) along with the loss calculated during training/validation of the model. The respective crossplots along with comparisons of ground truth vs. artificial intelligence (AI)-predicted curves indicated that the model is capable of making accurate predictions with an error percentage between 0.2% and 0.6% on history-matching experimental data for all three tested ML techniques. This implies that the AI-based model exhibits better efficiency and reliability in determining Kr curves when compared to conventional methods. The developed ML models by no means replace the need to conduct drainage coreflooding or centrifuge experiments but act as an alternative to existing commercial platforms that are used to interpret experimental data to predict Kr curves. The two main advantages of the developed ML models are their capability of predicting Kr curves within a matter of a few minutes as well as with limited intervention from the end user. The results also include a comparison between classical ML approaches, shallow neural networks, and DNNs in terms of accuracy in predicting the final Kr curves. The research presented here is an extension of the state-of-the-art framework proposed by Mathew et al. (2021). However, the two main aspects of the current study are the application of deep learning for the prediction of Kr curves and the application of feature engineering. The latter not only reduces the training/testing time for the ML models but also enables the end user to obtain the final predictions with the least set of experimental data. The various models discussed in this research work currently focus on the prediction of Kr curves for drainage steady-state experiments; however, the work can be extended to capture the imbibition cycle as well.

Fourier ptychography microscopy(FPM) is a recently developed computational imaging approach for microscopic super-resolution imaging. Nevertheless, FPM has high requirements for the system construction and data acquisition processes which brings many limitations to its practical applications. In this paper, we propose a Fourier ptychography multi-parameter neural network (FPMN) with composite physical prior optimization. A hybrid parameter determination strategy combining physical imaging model and data-driven network training is proposed to recover the multi layers of the network corresponding to different physical parameters, including sample complex function, system pupil function, defocus distance, LED array position deviation and illumination intensity fluctuation, etc. Among these parameters, LED array position deviation is recovered based on the features of brightfield to darkfield transition low-resolution images while the others are recovered in the process of training of the neural network. The feasibility and effectiveness of FPMN are verified through simulations and actual experiments. Therefore, FPMN can evidently reduce the requirement for practical applications of FPM.

Fourier ptychographic microscopy (FPM) is a computational approach geared towards creating high-resolution and large field-of-view images without mechanical scanning. Acquiring color images of histology slides often requires sequential acquisitions with red, green, and blue illuminations. The color reconstructions often suffer from coherent artifacts that are not presented in regular incoherent microscopy images. As a result, it remains a challenge to employ FPM for digital pathology applications, where resolution and color accuracy are of critical importance. Here we report a deep learning approach for performing unsupervised image-to-image translation of FPM reconstructions. A cycle-consistent adversarial network with multiscale structure similarity loss is trained to perform virtual brightfield and fluorescence staining of the recovered FPM images. In the training stage, we feed the network with two sets of unpaired images: (1) monochromatic FPM recovery and (2) color or fluorescence images captured using a regular microscope. In the inference stage, the network takes the FPM input and outputs a virtually stained image with reduced coherent artifacts and improved image quality. We test the approach on various samples with different staining protocols. High-quality color and fluorescence reconstructions validate its effectiveness.