Computation of Wavelet and Multiwavelet Transforms Using Fast Fourier Transform

A novel fast and efficient algorithm was proposed that uses the Fast Fourier Transform (FFT) as a tool to compute the Discrete Wavelet Transform (DWT) and Discrete Multiwavelet Transform. The Haar Wavelet Transform and the GHM system are shown to be a special case of the proposed algorithm, where the discrete linear convolution will adapt to achieve the desired approximation and detail coefficients. Assuming that no intermediate coefficients are canceled and no approximations are made, the algorithm will give the exact solution. Hence the proposed algorithm provides an efficient complexity verses accuracy tradeoff. The main advantages of the proposed algorithm is that high band and the low band coefficients can be exploited for several classes of signals resulting in very low computation.

Processing of strain gauge control signals by the Kalman filter

One of the methods for detecting defects in the rolling surface of the wheels of freight cars is to measure the deformations of the rail under the passing train. The method is based on the analysis of a strain gauge signal. The main task of the strain gauge signal analysis is the selection of informative components and the removal (filtering) of interference. The paper presents methods of filtering diagnostic signals of strain gauge control and the selection of informative components. The useful signal component can be used to measure the mass of cars, to determine the dynamic load on the rails and to detect defects in the rolling surface of the wheels. The method of adaptive Kalman filtering and linear convolution are proposed as signal processing tools. Based on these algorithms, a software module based on the.NET Framework has been developed using the C# programming language. The algorithms were tested on the signals received when the train was moving along the active section of the track, with a strain gauge control system located on it. The computational complexity and speed of the algorithms are assessed, and the possibility of their further application in the autonomous mode of the system is investigated. The results show that the use of the Kalman filtering algorithm provides a significant performance advantage over the linear convolution algorithm.

On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.

A Non-Linear Convolution Network for Image Processing

This paper proposes a new neural network structure for image processing whose convolutional layers, instead of using kernels with fixed coefficients, use space-variant coefficients. The adoption of this strategy allows the system to adapt its behavior according to the spatial characteristics of the input data. This type of layers performs, as we demonstrate, a non-linear transfer function. The features generated by these layers, compared to the ones generated by canonical CNN layers, are more complex and more suitable to fit to the local characteristics of the images. Networks composed by these non-linear layers offer performance comparable with or superior to the ones which use canonical Convolutional Networks, using fewer layers and a significantly lower number of features. Several applications of these newly conceived networks to classical image-processing problems are analyzed. In particular, we consider: Single-Image Super-Resolution (SISR), Edge-Preserving Smoothing (EPS), Noise Removal (NR), and JPEG artifacts removal (JAR).

Flat morphological operators from non-increasing set operators, I: general theory

Flat morphology is a general method for obtaining increasing operators on grey-level or multivalued images from increasing operators on binary images (or sets). It relies on threshold stacking and superposition; equivalently, Boolean max and min operations are replaced by lattice-theoretical sup and inf operations. In this paper we consider the construction a flat operator on grey-level or colour images from an operator on binary images that is not increasing. Here grey-level and colour images are functions from a space to an interval in ℝ m or ℤ m (m ≥ 1). Two approaches are proposed. First, we can replace threshold superposition by threshold summation. Next, we can decompose the non-increasing operator on binary images into a linear combination of increasing operators, then apply this linear combination to their flat extensions. Both methods require the operator to have bounded variation, and then both give the same result, which conforms to intuition. Our approach is very general, it can be applied to linear combinations of flat operators, or to linear convolution filters. Our work is based on a mathematical theory of summation of real-valued functions of one variable ranging in a poset. In a second paper, we will study some particular properties of non-increasing flat operators.

Assessment of Innovative Development of the Region Based on Comparative Analysis

The purpose of the paper is to determine the posi-tion of the Mari El Republic among the EU countries on innovative development. The study analyzes the innovation process in the field of R&D, high-tech sectors and digital society based on comparative analysis. A system of innovative development indi-cators has been developed. It includes three groups of indicators: R&D, innovation and conditions for the digitalization of the economy and society. The rating of innovative development has been built, which includes 28 EU countries, Russia and the Mari El Republic. The linear convolution of indicators is used to construct this rating. The position of the republic in the rating was determined and a compar-ative analysis of the Mari El Republic and the EU countries was carried out in terms of innovative de-velopment indicators. European countries have been identified that are comparable to the Mari El Repub-lic in terms of innovative development. Comparative analysis revealed good performance in R&D, as well as good human capacity and educational level of the population in the republic. There is a significant underfunding of science and innovation in the re-public compared to the European level. The dynam-ics of innovative development in the Mari El Repub-lic is insufficient for the innovation factor to become significant for its socio-economic development.

Some Algorithms for Computing Short-Length Linear Convolution

In this article, we propose a set of efficient algorithmic solutions for computing short linear convolutions focused on hardware implementation in VLSI. We consider convolutions for sequences of length N= 2, 3, 4, 5, 6, 7, and 8. Hardwired units that implement these algorithms can be used as building blocks when designing VLSI -based accelerators for more complex data processing systems. The proposed algorithms are focused on fully parallel hardware implementation, but compared to the naive approach to fully parallel hardware implementation, they require from 25% to about 60% less, depending on the length N and hardware multipliers. Since the multiplier takes up a much larger area on the chip than the adder and consumes more power, the proposed algorithms are resource-efficient and energy-efficient in terms of their hardware implementation.