Fourier phase retrieval algorithm based on deep denoiser network

Phase retrieval is an inverse problem which consists in recovering an unknown signal from a set of absolute squared projections. Recently, gradient descent algorithms have been developed to solve this problem. However, their optimization cost functions are non-convex and non-smooth. To address the non-smoothness of the cost function, some of these methods use truncation thresholds to calculate a truncated step gradient direction. But, the truncation requires designing parameters to obtain a desired performance in the phase recovery, which drastically modifies the search direction update, increasing the sampling complexity. Therefore, this paper develops the Phase Retrieval Smoothing Conjugate Gradient method (PR-SCG) which uses a smoothing function to retrieve the signal. PR-SCG is based on the smooth-ing projected gradient method which is useful for non-convex optimization problems. PR-SCG uses a nonlinear conjugate gradient of the smoothing function as the search direction to accelerate the convergence. Furthermore, the incremental Stochastic Smoothing Phase Retrieval algorithm (SSPR) is developed. SSPR involves a single equation per iteration which results in a simple, scalable, and fast approach useful when the size of the signal is large. Also, it is shown that SSPR converges linearly to the true signal, up to a global unimodular constant. Additionally, the proposed methods do not require truncation parameters. Simulation results are provided to validate the efficiency of PR-SCG and SSPR compared to existing phase retrieval algorithms. It is shown that PR-SCG and SSPR are able to reduce the number of measurements and iterations to recover the phase, compared with recently developed algorithms.

We study the eigenvalue distribution of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the analog of the population covariance matrix is now a function of random data matrices (synaptic weight matrices in the deep neural network terminology). The problem has been treated in recent work [J. Pennington, S. Schoenholz and S. Ganguli, The emergence of spectral universality in deep networks, Proc. Mach. Learn. Res. 84 (2018) 1924–1932, arXiv:1802.09979] by using the techniques of free probability theory. Since, however, free probability theory deals with population covariance matrices which are independent of the data matrices, its applicability in this case has to be justified. The justification has been given in [L. Pastur, On random matrices arising in deep neural networks: Gaussian case, Pure Appl. Funct. Anal. (2020), in press, arXiv:2001.06188] for Gaussian data matrices with independent entries, a standard analytical model of free probability, by using a version of the techniques of random matrix theory. In this paper, we use another version of the techniques to extend the results of [L. Pastur, On random matrices arising in deep neural networks: Gaussian case, Pure Appl. Funct. Anal. (2020), in press, arXiv:2001.06188] to the case where the entries of the data matrices are just independent identically distributed random variables with zero mean and finite fourth moment. This, in particular, justifies the mean field approximation in the infinite width limit for the deep untrained neural networks and the property of the macroscopic universality of random matrix theory in this case.

Phase retrieval is a promising method for optical system and surface metrology that makes use of intensity measurements of diffraction patterns. An iterative algorithm is used to solve the inverse problem to find the phase of the field producing the measured intensity distributions. For practical reasons, such as the reduction of coherent artifacts or to improve the signal-to-noise ratio of the measured data, it is often desirable to measure intensity distributions using broadband illumination. It is possible to perform phase retrieval with broadband data by incorporating a broadband model of the system into the phase retrieval algorithm. To do this, the system is modeled at several discrete wavelengths and the results from each are summed incoherently to produce a broadband result. This significantly increases the computational load. We show here that when aberrations are small, accurate estimates of the OPD distribution, on the level of λ/1000 RMS error, can be achieved using data with bandwidth up to about 10% as the input to a phase retrieval algorithm that assumes monochromatic data.

Phase retrieval, or the process of recovering phase information in reciprocal space to reconstruct images from measured intensity alone, is the underlying basis to a variety of imaging applications including coherent diffraction imaging (CDI). Typical phase retrieval algorithms are iterative in nature, and hence, are time-consuming and computationally expensive, making real-time imaging a challenge. Furthermore, iterative phase retrieval algorithms struggle to converge to the correct solution especially in the presence of strong phase structures. In this work, we demonstrate the training and testing of CDI NN, a pair of deep deconvolutional networks trained to predict structure and phase in real space of a 2D object from its corresponding far-field diffraction intensities alone. Once trained, CDI NN can invert a diffraction pattern to an image within a few milliseconds of compute time on a standard desktop machine, opening the door to real-time imaging.

Extracting and inserting knowledge into stacked denoising auto-encoders

Compared with conventional display technology, holographic projection technology has outstanding advantages. The phase retrieval algorithm is a key image processing algorithms in holographic projection technology. The constringency speed and precision of these algorithms need to be raised. The performance of the algorithms above are not satisfactory, sometimes they cannot even guarantee that the iterative process converges to the correct solutions. Then, this paper proposes a parallel architecture based on the phase recovery algorithm-Parallel Gerchberg-Saxton with Genetic Algorithm (PGSGA). Simulation has proved that the proposed algorithm PGSGA is better in convergence rate and the restoration quality by testing gray-scale image. K eywords: Holography; ViHPS; Phase Retrieval Algorithm; Phase-Only Hologram; GS Algorithm.

Transfer orthogonal sparsifying transform learning for phase retrieval

Phase retrieval for sub-Gaussian measurements

Purpose: The aim of the article is to develop an algorithm for classifying cracks in the analyzed images using modern methods of deep machine learning and transfer learning based on pretrained convolutional neural network - Inception-ResNet-v2. Design/Methodology/Approach: Transfer learning based on the pretrained convolutional neural network was used to categorize the images. The fully conected layer of the Inception-ResNet-v2 network has been modified. The last layer was trained using a two-class (binary) linear SVM (Support Vector Machine). In total, 20,000 training cases (images) were used to train the fully connected layer within transfer learning process. The research analyzed the possibility of using the deep neural networks for quick and fully automatic identification of cracks / defects on the surface of analyzed parts. Findings: The results indicate that pretrained convolutional neural network using SVM to train a fully connected layer is a very effective solution for visual crack / fault detection. In the analyzed model, a positive classification was obtained at the level of 99.89%. Practical Implications: The model presented in the article can be used in quality control carried out by process monitoring. An effective model for identifying defective parts can be used in both logistics and production processes. Originality/Value: A novelty is the use of a freely available, deep neural network trained to classify 1000 categories of various images for binary categorization of faults (cracks). The algorithm was adjusted by replacing the primary, 1000-output fully connected layer in the Inception-ResNet-v2 network with a binary layer (2 categories). The fully connected layer has been trained using the classification version of the popular SVM learner, but thanks to the combination of this layer with the sophisticated fearure extraction ability of the pre-trained Inception-ResNet-v2 deep network, the resulting predictive model enables the classification of defects with a very high level of accuracy.

We present a phase coefficient optimization technique for determining the vortex charge of a high-power orbital angular momentum beam. This high-power vortex beam is generated by transmitting a Gaussian-like beam emitted by a gyrotron with an output power of 25 kW through a spiral phase plate (SPP), which introduces a vorticity at the center of the beam characterized by the geometrical parameters of the SPP. One rigorous, intensity-measurement-based, phase retrieval technique, known as the Gerchberg–Saxton algorithm, does not converge to a correct solution because of the presence of a phase singularity in the high-power vortex beam. Here, we introduce a new phase retrieval algorithm that chooses an appropriate initial phase estimate. This technique yields successful vortex charge determination for both low- and high-power vortex beams. The retrieved intensity profiles show 99.51% and 99.27% intensity regeneration at measurement planes with optimized initial phase estimates for the low- and high-power beams, respectively.

Reconstruction of a stable and reliable solution from noisy and incomplete Fourier intensity data is a challenging problem for iterative phase retrieval algorithms. The typical methodology employed in the coherent X-ray imaging (CXI) literature involves thousands of iterations of well-known phase retrieval algorithms, e.g., hybrid input-output (HIO) or relaxed averaged alternating reflections (RAAR), that are concluded with a smaller number of error reduction (ER) iterations. Since the single run of this methodology may not provide a reliable solution, hundreds of trial solutions are first obtained by initializing the phase retrieval algorithm with independent random guesses. The resulting trial solutions are then averaged with appropriate phase adjustment, and resolution of the averaged reconstruction is assessed by plotting the phase retrieval transfer function (PRTF). In this work, we examine this commonly used RAAR-ER methodology from the perspective of the complexity parameter introduced by us in recent years. It is observed that the single run of the RAAR-ER algorithm provides a solution with undesirable grainy artifacts that persist to some extent even after averaging the multiple trial solutions. The grainy features are spurious in the sense that they are smaller in size compared to the resolution predicted by the PRTF curve. This inconsistency can be addressed by a novel methodology that we refer to as complexity-guided RAAR (CG-RAAR). The methodology is demonstrated with simulations and experimental data sets from the CXIDB database. In addition to providing consistent solution, CG-RAAR is also observed to require reduced number of independent trials for averaging.

Loan approval prediction is a critical task in the financial sector, enabling institutions to assess credit risk and make informed lending decisions. This research presents a comprehensive comparative study of various machine learning approaches for loan approval prediction, evaluating both traditional algorithms and deep learning architectures. We implemented and compared five traditional machine learning models (Logistic Regression, Decision Tree, Random Forest, Gradient Boosting, and SVM) against three neural network architectures (Simple Feed-Forward Neural Network, Deep Neural Network with Batch Normalization, and Wide & Deep Network). Using a synthetic dataset of 1,000 loan applications with features including income, credit score, and employment status, we achieved the highest accuracy of 93.5% with Gradient Boosting, closely followed by the Wide & Deep Neural Network at 93.5%. Feature importance analysis revealed credit score (45%) as the most influential factor, followed by income (40%) and employment status (15%). Additionally, we developed a professional Tkinter-based graphical user interface that enables real-time predictions, batch processing, and interactive visualizations. This system demonstrates the practical application of machine learning in financial decision-making and provides a framework for deploying predictive models in production environments. Keywords — Loan Approval, Machine Learning, Deep Learning, Neural Networks, Gradient Boosting, Tkinter GUI, Credit Risk Assessment

Domain-invariant representation learning using an unsupervised domain adversarial adaptation deep neural network

The raising number of elderly people urges the research of systems able to monitor and support people inside their domestic environment. An automatic system capturing data about the position of a person in the house, through accelerometers and RGBd cameras can monitor the person activities and produce outputs associating the movements to a given tasks or predicting the set of activities that will be executes. We considered, for the task the classification of the activities a Deep Convolutional Neural Network. We compared two different deep network and analyzed their outputs.

Accurate segmentation of the retinal microvasculature is a critical step in the quantitative analysis of the retinal circulation, which can be an important marker in evaluating the severity of retinal diseases. As manual segmentation remains the gold standard for segmentation of optical coherence tomography angiography (OCT-A) images, we present a method for automating the segmentation of OCT-A images using deep neural networks (DNNs). Eighty OCT-A images of the foveal region in 12 eyes from 6 healthy volunteers were acquired using a prototype OCT-A system and subsequently manually segmented. The automated segmentation of the blood vessels in the OCT-A images was then performed by classifying each pixel into vessel or nonvessel class using deep convolutional neural networks. When the automated results were compared against the manual segmentation results, a maximum mean accuracy of 0.83 was obtained. When the automated results were compared with inter and intrarater accuracies, the automated results were shown to be comparable to the human raters suggesting that segmentation using DNNs is comparable to a second manual rater. As manually segmenting the retinal microvasculature is a tedious task, having a reliable automated output such as automated segmentation by DNNs, is an important step in creating an automated output.