State-of-the-Art Approaches for Image Deconvolution Problems, including Modern Deep Learning Architectures

In modern digital microscopy, deconvolution methods are widely used to eliminate a number of image defects and increase resolution. In this review, we have divided these methods into classical, deep learning-based, and optimization-based methods. The review describes the major architectures of neural networks, such as convolutional and generative adversarial networks, autoencoders, various forms of recurrent networks, and the attention mechanism used for the deconvolution problem. Special attention is paid to deep learning as the most powerful and flexible modern approach. The review describes the major architectures of neural networks used for the deconvolution problem. We describe the difficulties in their application, such as the discrepancy between the standard loss functions and the visual content and the heterogeneity of the images. Next, we examine how to deal with this by introducing new loss functions, multiscale learning, and prior knowledge of visual content. In conclusion, a review of promising directions and further development of deconvolution methods in microscopy is given.

A MODIFIED METHOD OF SOLVING THE PRESSURE–RATE DECONVOLUTION PROBLEM FOR IDENTIFICATION OF WELLBORE–RESERVOIR SYSTEM

In the paper, the method suggested in [5] for solving the pressure–rate deconvo- lution problem was modified with implementation for the synthetic (quasi-real) oil and gas data. Modification of the method is based on using the additional a priori information on the function v(t) = tg(t) in the logarithmic scale. On the initial time interval, the function is concave and its final interval is monotone. Here, g(t) is the solution of the basis equation (1). To take into account these properties in the Tikhonov algorithm, the penalty function method is used. It allowed one to increase the precision of the numerical solution and to improve quality of identification of the wellbore–reservoir system. Numerical experiments are provided.

Measurement of Pulsatile Insulin Secretion: Rationale and Methodology

Pancreatic β-cells are responsible for the synthesis and exocytosis of insulin in response to an increase in circulating glucose. Insulin secretion occurs in a pulsatile manner, with oscillatory pulses superimposed on a basal secretion rate. Insulin pulses are a marker of β-cell health, and secretory parameters, such as pulse amplitude, time interval and frequency distribution, are impaired in obesity, aging and type 2 diabetes. In this review, we detail the mechanisms of insulin production and β-cell synchronization that regulate pulsatile insulin secretion, and we discuss the challenges to consider when measuring fast oscillatory secretion in vivo. These include the anatomical difficulties of measuring portal vein insulin noninvasively in humans before the hormone is extracted by the liver and quickly removed from the circulation. Peripheral concentrations of insulin or C-peptide, a peptide cosecreted with insulin, can be used to estimate their secretion profile, but mathematical deconvolution is required. Parametric and nonparametric approaches to the deconvolution problem are evaluated, alongside the assumptions and trade-offs required for their application in the quantification of unknown insulin secretory rates from known peripheral concentrations. Finally, we discuss the therapeutical implication of targeting impaired pulsatile secretion and its diagnostic value as an early indicator of β-cell stress.

Development of an Algorithm for Clustering Cardiac ECG Signals with Post-Correction for Long-Term ECG Monitoring

Introduction. The most common method for diagnosing cardiovascular diseases is the method of ECG monitoring. In order to facilitate the analysis of the obtained monitorograms, special software solutions for automated ECG processing are required. One possible approach is the use of algorithms for automated ECG processing. Such algorithms perform clustering of cardiac signals by dividing the ECG into complexes of similar cardiac signals. The most representative complexes obtained by statistical averaging are subject to further analysis.Aim. Development of an algorithm for automated ECG processing, which performs clustering of cardiac signals by dividing the ECG into complexes of similar cardiac signals.Materials and methods. Experimental testing of the developed software was carried out using patient records provided by the Pavlov First State Medical University of St Petersburg. The software module was implemented in the MatLab environment.Results. An algorithm for clustering cardiac signals with post-correction for the tasks of long-term ECG monitoring and a software module on its basis were proposed.Conclusion. The presence of a small number of reference cardiac signal complexes, obtained through ECG processing using the proposed algorithm, allows physicians to optimize the process of ECG analysis. The as- obtained information serves as a basis for assessing dynamic changes in the shape and other parameters of cardiac signals for both a particular patient and groups of patients. The paper considers the effect of synchronization errors of clustered cardiac signals on the shape of the averaged cardiac complex. The classical solution to the deconvolution problem leads to significant errors in finding an estimate of the true form of a cardiac signal complex. On the basis of analytical calculations, expressions were obtained for the correction of clustered cardiac signals. Such correction was shown to reduce clusterization errors associated with desynchronization, which creates a basis for investigating the fine structure of ECG signals.

Improved Approach for the Maximum Entropy Deconvolution Problem

The probability density function (pdf) valid for the Gaussian case is often applied for describing the convolutional noise pdf in the blind adaptive deconvolution problem, although it is known that it can be applied only at the latter stages of the deconvolution process, where the convolutional noise pdf tends to be approximately Gaussian. Recently, the deconvolutional noise pdf was approximated with the Edgeworth Expansion and with the Maximum Entropy density function for the 16 Quadrature Amplitude Modulation (QAM) input but no equalization performance improvement was seen for the hard channel case with the equalization algorithm based on the Maximum Entropy density function approach for the convolutional noise pdf compared with the original Maximum Entropy algorithm, while for the Edgeworth Expansion approximation technique, additional predefined parameters were needed in the algorithm. In this paper, the Generalized Gaussian density (GGD) function and the Edgeworth Expansion are applied for approximating the convolutional noise pdf for the 16 QAM input case, with no need for additional predefined parameters in the obtained equalization method. Simulation results indicate that improved equalization performance is obtained from the convergence time point of view of approximately 15,000 symbols for the hard channel case with our new proposed equalization method based on the new model for the convolutional noise pdf compared to the original Maximum Entropy algorithm. By convergence time, we mean the number of symbols required to reach a residual inter-symbol-interference (ISI) for which reliable decisions can be made on the equalized output sequence.

An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing

The dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more uneven, and the flatness cannot be further improved. In this paper, a reasonable elementary approximation algorithm of dwell time is proposed on the basis of the theoretical requirement of a removal function in the subaperture polishing and single-peak rotational symmetry character of its practical distribution. Then, the algorithm is well discussed with theoretical analysis and numerical simulation in cases of one-dimension and two-dimensions. In contrast to conventional dwell time algorithms, this proposed algorithm transforms superposition and coupling features of the deconvolution problem into an elementary approximation issue of function value. Compared with the conventional methods, it has obvious advantages for improving calculation efficiency and flatness, and is of great significance for the efficient computation of large-aperture optical polishing. The flatness of φ150 mm and φ100 mm workpieces have achieved PVr150 = 0.028 λ and PVcr100 = 0.014 λ respectively.

Through-Wall UWB Radar Based on Sparse Deconvolution with Arctangent Regularization for Locating Human Subjects

A common problem in through-wall radar is reflected signals much attenuated by wall and environmental noise. The reflected signal is a convolution product of a wavelet and an unknown object time series. This paper aims to extract the object time series from a noisy receiving signal of through-wall ultrawideband (UWB) radar by sparse deconvolution based on arctangent regularization. Arctangent regularization is one of the suitably nonconvex regularizations that can provide a reliable solution and more accuracy, compared with convex regularizations. An iterative technique for this deconvolution problem is derived by the majorization–minimization (MM) approach so that the problem can be solved efficiently. In the various experiments, sparse deconvolution with the arctangent regularization can identify human positions from the noisy received signals of through- wall UWB radar. Although the proposed method is an odd concept, the interest of this paper is in applying sparse deconvolution, based on arctangent regularization with an S-band UWB radar, to provide a more accurate detection of a human position behind a concrete wall.