Traditional Least-squares Fitting Research Articles

In vivo magnetic resonance P-Spectral Analysis With Neural Networks: 31P-SPAWNN.

We have introduced an artificial intelligence framework, 31P-SPAWNN, in order to fully analyze phosphorus-31 ( P) magnetic resonance spectra. The flexibility and speed of the technique rival traditional least-square fitting methods, with the performance of the two approaches, are compared in this work. Convolutional neural network architectures have been proposed for the analysis and quantification of P-spectroscopy. The generation of training and test data using a fully parameterized model is presented herein. In vivo unlocalized free induction decay and three-dimensional P-magnetic resonance spectroscopy imaging data were acquired from healthy volunteers before being quantified using either 31P-SPAWNN or traditional least-square fitting techniques. The presented experiment has demonstrated both the reliability and accuracy of 31P-SPAWNN for estimating metabolite concentrations and spectral parameters. Simulated test data showed improved quantification using 31P-SPAWNN compared with LCModel. In vivo data analysis revealed higher accuracy at low signal-to-noise ratio using 31P-SPAWNN, yet with equivalent precision. Processing time using 31P-SPAWNN can be further shortened up to two orders of magnitude. The accuracy, reliability, and computational speed of the method open new perspectives for integrating these applications in a clinical setting.

Artificial neural networks used to retrieve effective properties of metamaterials.

We propose using deep neural networks for the fast retrieval of effective properties of metamaterials based on their angular-dependent reflection and transmission spectra from thin slabs. While we noticed that non-uniqueness is an issue for a successful application, we propose as a solution an automatic algorithm to subdivide the entire parameter space. Then, in each sub-space, the mapping between the optical response (complex reflection and transmission coefficients) and the corresponding material parameters (dielectric permittivity and permeability) is unique. We show that we can easily train one neural network per sub-space. For the final parameter retrieval, predictions from the different sub-networks are compared, and the one with the smallest error expresses the desired effective properties. Our approach allows a significant reduction in run-time, compared to more traditional least-squares fitting. Using deep neural networks to retrieve effective properties of metamaterials is a significant showcase for the application of AI technology to nanophotonic problems. Once trained, the nets can be applied to retrieve properties of a larger number of different metamaterials.

A new short-arc fitting method with high precision using Adam optimization algorithm

The high-precision short-arc measurement is a huge challenge in scientific research and engineering practice. The popular traditional least square fitting (TLSF) however fails to achieve the precise fitting parameters when the arc gets shorter. In this work, an inequation constrained fitting (ICF) method based on four-parameter circle equation is presented. Lagrangian multiplier and Karush-Kuhn-Tucker criteria are used to redefine the objective function. After that, Adam algorithm is utilized to solve the objective function in iterative way. Adam algorithm has a strong ability to resist noise pollution by virtue of modifying continually the first-order momentum and second-order momentum with average of gradients during the course of iteration. Finally, simulation and experimental results show that our ICF method is more robust and high-precision than TLSF and Hyper method, so it is very competent to measure short arcs with noise even their central angles are close to 5°.

Phasor analysis of fluorescence lifetime data and its application

Fluorescence lifetime imaging microscopy (FLIM) is widely used in biomedical, materials and other fields. It not only has strong specificity and high sensitivity, but also has the capability of quantitative measurement because the fluorescence lifetime is not affected by the intensity of excitation, the concentration of fluorophores and photobleaching, and consequently is able to monitor the changes of microenvironment and reflecting the interaction between molecules. However, its application is limited to some extent by the complexity of data analysis. In order to make FLIM technology more suitable for fast analysis of high-throughput data, a variety of new algorithms for fluorescence lifetime analysis have emerged in recent years, such as phasor analysis, maximum likelihood estimation, first-order moment, Bayesian analysis, and compressed sensing. Among them, the phasor analysis (PA) method obtains the fluorescence lifetime by converting the fitting in the time domain to the direct calculation in the frequency domain. Compared with traditional least-square fitting method, it is not only simpler and faster, but also more suitable for the case of low photon counts. In addition, in the PA approach to FLIM, the fluorescence decay is directly converted into a phasor diagram by simple mathematics, where the phasor points originating from different pixels in the image are represented by the positions in the phasor plot, and thus the graphical representation obtained by PA method is convenient for data visualization and cluster analysis. Therefore, it has become a simple and powerful analysis method for FLIM, and is increasingly favored by researchers. In this paper, the basic principle of PA method and how we can use it are described in detail. And on this basis, the latest application research progress of the method in cell metabolism state measurement, protein interaction study, cell microenvironment measurement, auxiliary pathological diagnosis, and resolution improvement in super-resolution imaging are introduced and summarized. The advantages of PA method in these FLIM applications are focused on, providing useful reference for the research in related fields. Finally, the phasor analysis method for FLIM data analysis and the development trend of its application are prospected.

Deep spectral learning for label-free optical imaging oximetry with uncertainty quantification

Measurement of blood oxygen saturation (sO2) by optical imaging oximetry provides invaluable insight into local tissue functions and metabolism. Despite different embodiments and modalities, all label-free optical-imaging oximetry techniques utilize the same principle of sO2-dependent spectral contrast from haemoglobin. Traditional approaches for quantifying sO2 often rely on analytical models that are fitted by the spectral measurements. These approaches in practice suffer from uncertainties due to biological variability, tissue geometry, light scattering, systemic spectral bias, and variations in the experimental conditions. Here, we propose a new data-driven approach, termed deep spectral learning (DSL), to achieve oximetry that is highly robust to experimental variations and, more importantly, able to provide uncertainty quantification for each sO2 prediction. To demonstrate the robustness and generalizability of DSL, we analyse data from two visible light optical coherence tomography (vis-OCT) setups across two separate in vivo experiments on rat retinas. Predictions made by DSL are highly adaptive to experimental variabilities as well as the depth-dependent backscattering spectra. Two neural-network-based models are tested and compared with the traditional least-squares fitting (LSF) method. The DSL-predicted sO2 shows significantly lower mean-square errors than those of the LSF. For the first time, we have demonstrated en face maps of retinal oximetry along with a pixel-wise confidence assessment. Our DSL overcomes several limitations of traditional approaches and provides a more flexible, robust, and reliable deep learning approach for in vivo non-invasive label-free optical oximetry.