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Wavelets are actively used to solve a wide range of image processing problems in various fields of science and technology. Modern image processing systems cannot keep up with the rapid growth in digital visual information. Various approaches are used to reduce the computational complexity and increase computational speeds. The Winograd method (WM) is one of the most promising. However, this method is used to obtain sequential values. Its use for wavelet image processing requires expanding the calculation methodology to cases of downsampling. This paper proposes a new approach to reduce the computational complexity of wavelet image processing based on the WM with decimation. Calculations have been carried out and formulas have been derived that implement digital filtering using the WM with downsampling. The derived formulas can be used for 1D filtering with an arbitrary downsampling stride. Hardware modeling of wavelet image filtering on an FPGA showed that the WM reduces the computational time by up to 66%, with increases in the hardware costs and power consumption of 95% and 344%, respectively, compared to the direct method. A promising direction for further research is the implementation of the developed approach on ASIC and the use of modular computing for more efficient parallelization of calculations and an even greater increase in the device speed. [ABSTRACT FROM AUTHOR]

The main goal of machine learning is the creation of self-learning algorithms in many areas of human activity. It allows a replacement of a person with artificial intelligence in seeking to expand production. The theory of artificial neural networks, which have already replaced humans in many problems, remains the most well-utilized branch of machine learning. Thus, one must select appropriate neural network architectures, data processing, and advanced applied mathematics tools. A common challenge for these networks is achieving the highest accuracy in a short time. This problem is solved by modifying networks and improving data pre-processing, where accuracy increases along with training time. Bt using optimization methods, one can improve the accuracy without increasing the time. In this review, we consider all existing optimization algorithms that meet in neural networks. We present modifications of optimization algorithms of the first, second, and information-geometric order, which are related to information geometry for Fisher–Rao and Bregman metrics. These optimizers have significantly influenced the development of neural networks through geometric and probabilistic tools. We present applications of all the given optimization algorithms, considering the types of neural networks. After that, we show ways to develop optimization algorithms in further research using modern neural networks. Fractional order, bilevel, and gradient-free optimizers can replace classical gradient-based optimizers. Such approaches are induced in graph, spiking, complex-valued, quantum, and wavelet neural networks. Besides pattern recognition, time series prediction, and object detection, there are many other applications in machine learning: quantum computations, partial differential, and integrodifferential equations, and stochastic processes. [ABSTRACT FROM AUTHOR]

The high accuracy attainment, using less complex architectures of neural networks, remains one of the most important problems in machine learning. In many studies, increasing the quality of recognition and prediction is obtained by extending neural networks with usual or special neurons, which significantly increases the time of training. However, engaging an optimization algorithm, which gives us a value of the loss function in the neighborhood of global minimum, can reduce the number of layers and epochs. In this work, we explore the extreme searching of multidimensional functions by proposed natural gradient descent based on Dirichlet and generalized Dirichlet distributions. The natural gradient is based on describing a multidimensional surface with probability distributions, which allows us to reduce the change in the accuracy of gradient and step size. The proposed algorithm is equipped with step-size adaptation, which allows it to obtain higher accuracy, taking a small number of iterations in the process of minimization, compared with the usual gradient descent and adaptive moment estimate. We provide experiments on test functions in four- and three-dimensional spaces, where natural gradient descent proves its ability to converge in the neighborhood of global minimum. Such an approach can find its application in minimizing the loss function in various types of neural networks, such as convolution, recurrent, spiking and quantum networks. [ABSTRACT FROM AUTHOR]

Simple Summary: Skin cancer is one of the most common cancers in humans. This study aims to create a system for recognizing pigmented skin lesions by analyzing heterogeneous data based on a multimodal neural network. Fusing patient statistics and multidimensional visual data allows for finding additional links between dermoscopic images and medical diagnostic results, significantly improving neural network classification accuracy. The use by specialists of the proposed system of neural network recognition of pigmented skin lesions will enhance the efficiency of diagnosis compared to visual diagnostic methods. Today, skin cancer is one of the most common malignant neoplasms in the human body. Diagnosis of pigmented lesions is challenging even for experienced dermatologists due to the wide range of morphological manifestations. Artificial intelligence technologies are capable of equaling and even surpassing the capabilities of a dermatologist in terms of efficiency. The main problem of implementing intellectual analysis systems is low accuracy. One of the possible ways to increase this indicator is using stages of preliminary processing of visual data and the use of heterogeneous data. The article proposes a multimodal neural network system for identifying pigmented skin lesions with a preliminary identification, and removing hair from dermatoscopic images. The novelty of the proposed system lies in the joint use of the stage of preliminary cleaning of hair structures and a multimodal neural network system for the analysis of heterogeneous data. The accuracy of pigmented skin lesions recognition in 10 diagnostically significant categories in the proposed system was 83.6%. The use of the proposed system by dermatologists as an auxiliary diagnostic method will minimize the impact of the human factor, assist in making medical decisions, and expand the possibilities of early detection of skin cancer. [ABSTRACT FROM AUTHOR]

• A new sign detection method based on the Chinese Remainder Theorem (CRT) with fractional values implemented using the Wallace tree and the modified Kogge-Stone adder was proposed. • Hardware modelling on FPGA for the proposed method shows that it provides 1.3 36.3 times less hardware costs than the other state-of-the-art (SOTA) methods. • ASIC modelling for the proposed method provides 1.14 35.74 times less hardware costs than the other SOTA methods. • The presented sign detection method can be helpful in RNS-based devices in implementing comparison and division operations. Sign detection is a non-modular operation in the residue number system (RNS). It requires the calculation of the number positional characteristic represented in the RNS. This work proposes a new sign detection method based on the Chinese Remainder Theorem (CRT) with fractional values implemented using the Wallace tree and the modified Kogge-Stone adder. Hardware modelling on FPGA for the proposed method shows that it provides 1.3 – 36.3 times less hardware costs than the other state-of-the-art (SOTA) methods, and for ASIC modelling the proposed method provides 1.14 – 35.74 times less hardware costs than the other SOTA methods. The presented sign detection method can be helpful in RNS-based devices in implementing comparison and division operations, providing an extension of the RNS application in areas such as cryptography, machine learning, and digital signal processing. [ABSTRACT FROM AUTHOR]