Operation Of Convolution Research Articles

Feature ensemble network for medical image segmentation with multi‐scale atrous transformer

AbstractRecent years have witnessed notable advancements in medical image segmentation through deep convolutional neural networks. However, a notable limitation lies in the local operation of convolution, which hinders the ability to fully exploit global semantic information. To overcome the challenges prevalent in medical image segmentation, the feature ensemble network with multi‐scale atrous transformer is proposed. At the core of the approach lies the multi‐scale contextual integration module, which is based on the multi‐scale atrous transformer and facilitates contextual integration of multi‐level features. To extract discriminative fine‐grained features of the target region, a hybrid attention mechanism that synergistically combines spatial and channel attention, thereby sharpening the model's focus on crucial target information within high‐level features, is incorporated. Additionally, the channel‐aware feature reconstruction module is introduced as an innovative component engineered to tackle feature similarity issues across different categories. This module performs feature reconstruction based on channel perception, effectively widening the feature gap between categories and enhancing the segmentation capability. It is worth mentioning that our approach surpasses the state‐of‐the‐art method using three benchmark datasets in medical image segmentation.

Research on an underwater image segmentation algorithm based on YOLOv8

Underwater image segmentation faces complex problems such as target type, number, scale, and environmental interference. The traditional segmentation method relies on much manual annotation and expertise, extracts only the surface information of the image, and has low segmentation accuracy and efficiency, so the image segmentation method based on deep learning is chosen. Deep learning algorithms are used on top of the YOLOv8, and the adaptive self-supervised learning (Convnext V2) module, the lightweight network (Slim Neck), and the dynamic sparse attention mechanism (bilevel routing attention, Biformer) are added, which improves the YOLOv8 algorithm for single-stage instance segmentation of different underwater targets. The Convnext V2 module introduces the global response normalization (GRN) unit, which enhances the feature competition and reduces the model computation. A slim neck network is designed, which achieves a double improvement in model inference speed and accuracy by the operation of dense convolution in the lightweight convolution (GSConv) module and the design of a cross-level network structure (VoV-GSCSP). The introduction of Biformer’s dynamic sparse attention mechanism achieves more flexible computational allocation and content awareness. Comparison experiments show that the improved algorithm dramatically increases the segmentation speed while improving the segmentation accuracy. On the dual-target dataset, the mAP is improved by 3.5% from 0.753 to 0.779, and the FPS is improved by 86% from 63 to 117. The experiments validate that the improved algorithm can be used for the segmentation of different underwater images.

Quantum Rényi entropy functionals for bosonic Gaussian systems

In this study, the quantum Rényi entropy power inequality of order p>1 and power κ is introduced as a quantum analog of the classical Rényi-p entropy power inequality. To derive this inequality, we first exploit the Wehrl-p entropy power inequality on bosonic Gaussian systems via the mixing operation of quantum convolution, which is a generalized beam-splitter operation. This observation directly provides a quantum Rényi-p entropy power inequality over a quasi-probability distribution for D-mode bosonic Gaussian regimes. The proposed inequality is expected to be useful for the nontrivial computing of quantum channel capacities, particularly universal upper bounds on bosonic Gaussian quantum channels, and a Gaussian entanglement witness in the case of Gaussian amplifier via squeezing operations.

OPTIMAL CONTROL OF A DYNAMIC SYSTEM WITH NON-SEPARADED POINT AND INTEGRAL CONDITIONS

. In the work, a numerical method is proposed to solve a system of linear nonautonomous ordinary differential equations with non-separated multipoint and integral conditions. The proposed approach is based on the introduced operation of convolution of integral conditions into local ones. The method allows to reduce the solution of the original problem to the solution of Cauchy problem with respect to a system of ordinary differential equations and of linear algebraic equations. The stability of the computational schemes is shown.

End-to-End Training of Deep Neural Networks in the Fourier Domain

Convolutional networks are commonly used in various machine learning tasks, and they are more and more popularly used in the embedded domain with devices such as smart cameras and mobile phones. The operation of convolution can be substituted by point-wise multiplication in the Fourier domain, which can save operation, but usually, it is applied with a Fourier transform before and an inverse Fourier transform after the multiplication, since other operations in neural networks cannot be implemented efficiently in the Fourier domain. In this paper, we will present a method for implementing neural network completely in the Fourier domain, and by this, saving multiplications and the operations of inverse Fourier transformations. Our method can decrease the number of operations by four times the number of pixels in the convolutional kernel with only a minor decrease in accuracy, for example, 4% on the MNIST and 2% on the HADB datasets.

Synthesis of a mathematical model of the transformation core for processing vibroseismic data by reverse filtering

The vibroseismic method of studying the bowels of the earth is widely used to study the structural features of the bowels. The effectiveness of the method is due to the presence of controlled sources of seismic waves. In this case, the sources of seismic waves form a seismic signal, the parameters of which are determined and set by the researcher during the planning of the experiment. Frequency-modulated seismic signals - sweep signals - have become the most popular in field seismology. A special case of these signals are monochromatic signals. During the experiment, the seismic signal generated by the source is recorded by a seismic receiver. Thus, the researcher receives the initial seismic record - a seismogram. Processing of a seismogram, as an element of vibroseismic data, assumes the presence of information about the parameters of the seismic signal of the source. Based on this signal, a conversion core is formed for processing the seismogram. As a result of the operation of convolution of the seismogram with the core of the transformation, a vibrogram is formed. If it is necessary to increase the contrast (resolution) of the vibrogram, an additional filtering function is introduced into the conversion core, which performs the reverse filtering procedure. The purpose of this study is to form a filtering function and a mathematical model of the transformation core, which allows to increase the contrast of the vibrogram. The structurality and simplicity of the analytical expressions of the filtering function and the mathematical model of the transformation kernel is achieved by representing the function and model in operator form by means of the Laplace transform. The result of the study is analytical expressions in the operator form of the filtering function and a mathematical model of the transformation core to increase the contrast of vibrograms.

Human activity recognition using wearable sensors by heterogeneous convolutional neural networks

Recent researches on sensor based human activity recognition (HAR) are mostly devoted to designing various network architectures to enhance their feature representation capacity for raw sensor data. In this paper, we focus on strengthening the vanilla convolution without adjusting the model architectures in HAR scenario. Inspired by the idea of grouped convolution, we propose a novel heterogeneous convolution for activity recognition task, where all filters within a specific convolutional layer are separated into two uneven groups. Specifically, the sensor input is down-sampled into a low-dimensional embedding, which is then convolved by one filter group to recalibrate normal filters within the other group. The two filter groups can complement each other, which is very beneficial for augmenting the receptive field of sensor signals for HAR task. Extensive experiments are conducted on several benchmark HAR datasets, which consists of OPPORTUNITY, PAMAP2, UCI-HAR, USC-HAD as well as the Weakly Labeled HAR dataset. The results show that the baseline models can be significantly improved. Our heterogeneous convolution is simple and can easily be integrated into standard convolutional layers without increasing extra parameters and computational overhead. Finally, the actual operation of heterogeneous convolution is evaluated on an embedded Raspberry Pi platform.

Facial Expression Recognition Based on Deep Binary Convolutional Network

Facial expression recognition (FER) is a challenging task because of the large number of parameters, low speed and insufficient feature representation of the expression region. In order to address the above-mentioned challenges, a deep binary convolutional network for FER is proposed. Firstly, a lightweight convolution network (BRNet) with parallel operation of binary convolution and traditional convolution is designed to reduce the complexity of network and improve the speed of recognition. Secondly, a dynamic radius strategy is constructed to extract binary features and form the attention weight of expression region so that the local features and global features can be fused effectively. Finally, the cross-entropy and <italic>L</italic>₂ loss are designed for quick and accurate expression classification. Experiments show that the average accuracy of the proposed method is 99.25% and 93.85% on CK+ and Oulu-CASIA respectively, which are higher than the other similar lightweight convolutional networks. The parameters and computation cost of network are 5.0×10⁵ bytes and 2.1×10⁶ bytes. In contrast, the computation cost of EfficientFace is about 77 times than proposed method. As a result, the effectiveness and lightness of proposed method have been proved.

Efficient Small-Object Detection in Airport Surface Based on Maintain Feature High Resolution

Detection of small objects is a challenge in computer vision, especially in the application of airport surface surveillance. Operation of convolution is the key to losing the semantic information of small objects. In this paper, a high-resolution network is designed to maintain the feature information of small objects. Channel restructuring is used to enlarge the feature map and merge it with the shallow feature map to enhance the feature position information, rather than bilinear interpolation upsampling in traditional methods. Experiments show that, in the self-built airport surface dataset, compared with the mainstream object detector Fully Convolutional One-Stage Object Detector, RetinaNet, and other methods, the proposed method can reach the state-of-the-art in various precision indexes. In terms of model size and number of parameters, the proposed method is significantly smaller than Faster Region-Convolutional Neural Networks. Under the same input size, compared with You Only Look Once v3, the method presented in this paper can obtain a lower number of parameters and a faster inference speed. In the case of using GTX1080Ti, our method can reach 76.7 frames per second.

1S-1R array: Pure-memristor circuit for binary neural networks

In order to achieve the transistor-less circuit, which has remarkable potentials for high speed, high-density integration, and low power consumption applications, a 1-selector−1-resistor (1S − 1R) structure is utilized in this work to replace the prevalent 1-transistor−1-resistor (1T − 1R) array of memristor synaptic architectures. The 1S − 1R structure consists of a four-terminal memristor acting as a selector and a two-terminal memristor storing information in the form of device resistances. The high resistance state (HRS) and the low resistance state (LRS) of two-terminal memristor are used in conjunction to represent binary weight in binary neural networks (BNN), and multiply-accumulate operation of convolution can be replaced by the current accumulation of the 1S − 1R circuit. With the purpose of mapping binary weights into the 1S − 1R array to implement the forward propagation at the circuit simulation level, a LeNet model has been modified herein where two full-precision convolution layers are replaced by two binary convolutional layers. Compared with the full-precision LeNet model, the storage resource consumption of the binarized network is reduced by 44.28%, while the accuracy can reach 98% in 10 epochs, which is very close to the full-precision network. The 1S − 1R array is used subsequently to store the binary weight of a convolution layer in the trained LeNet and 100 pictures with numbers 0 to 9 in MNIST are randomly selected for testing. As expected, the result obtained through circuit simulation is consistent with the convolution operation in the process of forward propagation.

Identifying piRNA targets on mRNAs in C. elegans using a deep multi-head attention network

BackgroundPiwi-interacting RNAs (piRNAs) are the small non-coding RNAs (ncRNAs) that silence genomic transposable elements. And researchers found out that piRNA also regulates various endogenous transcripts. However, there is no systematic understanding of the piRNA binding patterns and how piRNA targets genes. While various prediction methods have been developed for other similar ncRNAs (e.g., miRNAs), piRNA holds distinctive characteristics and requires its own computational model for binding target prediction.ResultsRecently, transcriptome-wide piRNA binding events in C. elegans were probed by PRG-1 CLASH experiments. Based on the probed piRNA-messenger RNAs (mRNAs) binding pairs, in this research, we devised the first deep learning architecture based on multi-head attention to computationally identify piRNA targeting mRNA sites. In the devised deep network, the given piRNA and mRNA segment sequences are first one-hot encoded and undergo a combined operation of convolution and squeezing-extraction to unravel motif patterns. And we incorporate a novel multi-head attention sub-network to extract the hidden piRNA binding rules that can simulate the biological piRNA target recognition process. Finally, the true piRNA–mRNA binding pairs are identified by a deep fully connected sub-network. Our model obtains a supreme discriminatory power of AUC = 93.3% on an independent test set and successfully extracts the verified binding pattern of a synthetic piRNA. These results demonstrated that the devised model achieves high prediction performance and suggests testable potential biological piRNA binding rules.ConclusionsIn this research, we developed the first deep learning method to identify piRNA targeting sites on C. elegans mRNAs. And the developed deep learning method is demonstrated to be of high accuracy and can provide biological insights into piRNA–mRNA binding patterns. The piRNA binding target identification network can be downloaded from http://cosbi2.ee.ncku.edu.tw/data_download/piRNA_mRNA_binding.

Optimization of Multi-Criterial Selection Algorithm with a Dynamically Filled Large Set of Alternatives

We consider the problem of the correct ranking of a dynamically replenished large set of alternatives in multicriteria choice problems that use in the solution the previously obtained modified method for analyzing hierarchies, based on the operation of additive convolution of local priorities not on the obtained set of characteristics of paired comparison matrices (as in the classical method), but on a set of pairs the relative weights of the coordinates of the eigenvectors being compared with each other for each criterion and the subsequent operation of additive convolution according to the criteria and alternatives in each pair. In this version, the algorithm ensures that previously achieved preferences are preserved when adding new alternatives and, thereby, makes it possible to optimize when processing large volumes of dynamically changing data, which significantly expands the applicability of the popular algorithm.

Q-Binomial Convolution and Transformations of q-Appell Polynomials

In this paper, binomial convolution in the frame of quantum calculus is studied for the set Aq of q-Appell sequences. It has been shown that the set Aq of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure Aq have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences.

A Cascaded Feature Pyramid Network With Non-Backward Propagation for Facial Expression Recognition

In this work we propose a novel cascaded feature pyramid network with non-backward propagation (CFPN-NBP) for facial expression recognition (FER) that addresses the problems inherent in traditional backward propagation (BP) algorithms in the training process by using the Hilbert-Schmidt independence criterion (HSIC) bottleneck. The proposed algorithm is developed at two different levels. At the first level, a novel training method HSIC bottleneck is considered as an alternative to traditional BP optimization, where the correlation between the output of the hidden layers and the input, and the correlation between the output of the hidden layers and its label are calculated to reduce redundant information; hence, the least information is used to predict the results. At the second level, a novel architecture is designed in the feature extraction process. The convolutional layers with the same resolutions are densely connected and introduced into the attention mechanism, so that the model can focus on more important information. The convolutional layers with different resolutions are combined by three cascaded pyramid networks; in this way, the shallow features and the deep features can be further fused, and; therefore, the semantic information and the content information can both be reserved. To further reduce the number of parameters, the operation of separable convolution instead of traditional convolution is utilized. Experiments on the challenging FER2013 dataset show that the proposed CFPN-NBP algorithm improves the accuracy of the FER task and outperforms the related state-of-the-art methods.

Blind deconvolution of covariance matrix inverses for autoregressive processes

Matrix C can be blindly deconvoluted if there exist matrices A and B such that C=A⁎B, where ⁎ denotes the operation of matrix convolution. We study the problem of matrix deconvolution in the case where matrix C is proportional to the inverse of the autocovariance matrix of an autoregressive process. We show that the deconvolution of such matrices is important in problems of Hankel structured low-rank approximation (HSLRA). In the cases of autoregressive models of orders one and two, we fully characterize the range of parameters where such deconvolution can be performed and provide construction schemes for performing deconvolutions. We also consider general autoregressive models of order p, where we prove that the deconvolution C=A⁎B does not exist if the matrix B is diagonal and its size is larger than p.

Binary Outer Product Expansion of Convolutional Kernels

Convolutional neural networks (CNNs) have found great success in many artificial intelligence applications. At the heart of a CNN is the operation of convolution between multi-channel data and learned kernels. It is usually implemented as a floating-point large matrix multiplication, a major bottleneck of computational speed and memory usage. In this paper, we propose a binary outer product expansion (BOPE) method to represent a kernel matrix or tensor as a weighted sum of the outer products between binary vectors of values +1 or −1. This allows for network compression and simplified computation at the same time. Our theoretical analysis shows such a decomposition converges to the original matrix given a sufficient number of binary vectors. We present computational methods to estimate outer product weights using either optimized or random binary base vectors. Significant data compression can be achieved for a highly redundant matrix, since weights and binary vectors require less storage than array elements. In addition, most floating-point multiplication in matrix convolution can be replaced by addition and binary XOR, lessening computation and memory requirements. We propose a compact convolutional layer in which highly redundant convolutional kernels are projected onto binary vectors, and represented as a weighted sum of outer products. It is shown that the number of weights in AlexNet, VGG−19 and ResNet-50 can be reduced 3.45, 6.87 and 2.95 times respectively with less than a 1% loss in the top-1 and top-5 classification accuracy on ImageNet, and MobileNetV2 can be reduced 2.31 times with a 2% loss. Compared to the standard CNN, this compact convolutional network has fewer trainable weights, is better regularized, and is easier to train from fewer training samples. Therefore, it is particularly suited for devices with limited computation, memory, and battery power.

АЛГОРИТМЫ ПЕРВИЧНОЙ И ВТОРИЧНОЙ ОБРАБОТКИ СИГНАЛОВ В СИСТЕМАХ АКТИВНОГО АПЕРТУРНОГО СИНТЕЗА

A method for processing spatio-temporal radio signals, which allows the formation of high spatial resolution images from aerospace carriers, has been synthesized. In this case, a swath is ±15° from the nadir relative to the flight line is considered. Traditionally this swath is not visible from aerospace carriers. A block diagram of an active-passive type radar is proposed. Initially the image obtained at the output of such a radar has a low quality of visual perception. Such image is called primary, since it was obtained at the stage of primary signal processing. The physical sense of such image is investigated. It approximately represents the operation of convolution of the ambiguity function with a spatial function proportional to the ideal image. The physical sense of the ideal image depends on the characteristics of the imaging system. In the problem under consideration, this is the specific radar cross section. In order to improve the quality of the image it is proposed additional processing (filtering). The paper substantiates the method of filtering (secondary processing) of images based on the solution of the inverse integral equation. It is shown that the exact solution to this equation is difficult to obtain because the form of the ambiguity function is not known exactly and can be estimated only approximately and, in addition, not for each ambiguity function it is possible to obtain a non-singular solution of the inversion equation. Therefore, an approximate solution to the problem is given. It solution is sufficient to solve practical problems of improving image quality. Using numerical simulation methods, the influence of the error in determining the shape of the uncertainty function on the task of improving image quality is studied. Examples of primary and secondary images obtained at the output of wideband active aperture synthesis systems with various geometries of spatially distributed antenna systems are given.

Deep multiple classifier fusion for traffic scene recognition

The recognition of the traffic scene in still images is an important yet difficult task in an intelligent transportation systems. The main difficulty lies in how to improve the image processing algorithms for different traffic participants and the various layouts of roads while discriminating the different traffic scenes. In this paper, we attempt to solve the traffic scene recognition problem with three distinct contributions. First, we propose a deep multi-classifier fusion method in the setting of granular computing. Specifically, the deep multi-classifier fusion method which involves local deep-learned feature extraction at one end that is connected to the other end for classification through a multi-classifier fusion approach. At the local deep-learned feature extraction end, the operation of convolution to extract feature maps from the local patches of an image is essentially a form of information granulation, whereas the fusion of classifiers at the classification end is essentially a form of organization. The second contribution is the creation of new traffic scene data set, named the “WZ-traffic”. The WZ-traffic data set consists of 6035 labeled images, which belong to 20 categories collected from both an image search engine as well as from personal photographs. Third, we make extensive comparisons with state-of-the-art methods on the WZ-traffic and FM2 data sets. The experiment results demonstrate that our method dramatically improves traffic scene recognition and brings potential benefits to many other real-world applications.

Persistent homology and microlocal sheaf theory

We interpret some results of persistent homology and barcodes (in any dimension) with the language of microlocal sheaf theory. For that purpose we study the derived category of sheaves on a real finite-dimensional vector space V. By using the operation of convolution, we introduce a pseudo-distance on this category and prove in particular a stability result for direct images. Then we assume that V is endowed with a closed convex proper cone $\gamma$ with non empty interior and study $\gamma$-sheaves, that is, constructible sheaves with microsupport contained in the antipodal to the polar cone (equivalently, constructible sheaves for the $\gamma$-topology). We prove that such sheaves may be approximated (for the pseudo-distance) by "piecewise linear" $\gamma$-sheaves. Finally we show that these last sheaves are constant on stratifications by $\gamma$-locally closed sets, an analogue of barcodes in higher dimension.

Closed form expressions for Appell polynomials

We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually multipliers in the abelian group of the Appell polynomials endowed with the operation of binomial convolution. As a consequence, we obtain explicit expressions for higher order convolution identities referring to various kinds of Appell polynomials in terms of the Stirling numbers. Applications of the preceding results to generalized Bernoulli and Apostol–Euler polynomials of real order are discussed in detail.