Kiyotaka Kohno, Mitsuru Kawamoto, Yujiro Inouye · 2010
The matrix inversion lemma gives an explicit formula of the inverse of a positive-definite matrix A added to a block of dyads (represented as BB <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sup> ). It is well-known in the literature that this formula is very useful to develop a block-based recursive least-squares algorithm for the block-based recursive identification of linear systems or the design of adaptive filters. We already extended this result to the case when the matrix A is singular, and presented the matrix pseudo-inversion lemma. Such a singular case may occur in a situation where a given problem is overdetermined in the sense that it has more equations than unknowns. In this paper, based on these results, we propose a block-based adaptive multichannel super-exponential deflation algorithm. We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudo-inversion lemma.
Cited by 2
Lin Wang, Siqi Yang, Jingqian Jia · 2020
Super-resolution reconstruction is a technique for recovering corresponding high-resolution images from low-resolution images. Aiming at the problem of insufficient learning ability of the generative network in the SRGAN, a super-resolution reconstruction algorithm of generative adversarial network based on feature fusion is proposed. Recursive residual networks and prior knowledge are used to extract edge and texture features, while densely connected networks are used to fully utilize the features. Aiming at the problem that the input of the discriminative network of the SRGAN has a high computational complexity for the entire image, a method for discriminant residual discrimination is proposed. Two difference maps are used as input images of the discriminative network, and two discriminative methods are used for training. The test data set was used to verify the performance of the algorithm. The subjective index was significantly better than the original algorithm. The objective index PSNR increased by 0.77db, and SSIM increased by 2.8%.
Cited by 1
Qing Zhao, Zhi Xu, Lei Yang · Applied Sciences · 2023
Location information is one of the crucial and essential elements for monitoring data in wireless sensor networks. The distance vector-hop (DV-Hop) localization algorithm is of practical importance in improving its localization performance. To achieve global optimization, a DV-Hop algorithm based on the cyclotomic method and weighted normalization, also known as CMWN-DV-Hop, is nominated in this paper. Therefore, the segmentation and weighting factors are introduced and normalized. The weighted recursive least-squares (WRLS) algorithm is chosen to compute the coordinates of the unknown nodes. The effects of various factors on this algorithm are tested, including the number of nodes, the anchor node ratio, and the communication radius. The simulation results show that the proposed algorithm has a super performance in reducing the localization error.
Cited by 24Open access
Jannik Olbrich, Enno Ohlebusch, Thomas Büchler · arXiv (Cornell University) · 2022
The suffix array is arguably one of the most important data structures in sequence analysis and consequently there is a multitude of suffix sorting algorithms. However, to this date the GSACA algorithm introduced in 2015 is the only known non-recursive linear-time suffix array construction algorithm (SACA). Despite its interesting theoretical properties, there has been little effort in improving the algorithm's subpar real-world performance. There is a super-linear algorithm DSH which relies on the same sorting principle and is faster than DivSufSort, the fastest SACA for over a decade. This paper is concerned with analysing the sorting principle used in GSACA and DSH and exploiting its properties in order to give an optimised linear-time algorithm. Our resulting algorithm is not only significantly faster than GSACA but also outperforms DivSufSort and DSH.
Cited by 1Open access
Haohao Du, Chenghu Jing, Bingsheng Yan et al. · Mechanika · 2023
In this paper, a passive-based adaptive robust super-twisting nonlinear controller (PBARSNC) is proposed for high accuracy torque tracking control of the novel electro-hydraulic loading system with disturbances and uncertainties. The construction of the stability of this electro-hydraulic control system is given using passivity theory that results in a passivity-based controller (PBC). Considering parameter uncertainties and constant or slowly varying disturbances, adaptive law is adopted in the passivity-based controller. Furthermore, super-twisting second-order sliding mode control is used to reject modeling uncertainties and matched disturbances. Passivity theory, adaptive method and super-twisting algorithm are synthesized via the recursive design method. The proposed passive-based adaptive robust super-twisting nonlinear control can guarantee the torque tracking performance in the presence of various uncertainties, which is very important for high-accuracy tracking control of hydraulic servo systems. Extensive simulations are carried out to verify the high-accuracy tracking performance of the proposed control strategy.
Cited by 1Open access
Yuxing Yang, Kaiyue Meng · Research Square · 2023
Abstract The hypercube and the $k$-ary $n$-cube are two leading interconnection networks for multiprocessor systems. {\it A $t$-embedded edge cut} of an $n$-dimensional recursive interconnection network $G_n$ is a set of edges whose removal separates $G_n$ and each vertex lies in a $t$-dimensional subnetwork of the residual network. The network $G_n$ is {\it super $t$-embedded edge connected} ({\it super-$\eta_t$} for short) if the deletion of an arbitrary minimum $t$-embedded edge cut of $G_n$ isolates a $t$-dimensional subnetwork $G_t$. In this note, we show that both the $n$-dimensional hypercube and the ternary $n$-cube are super-$\eta_t$ for $0\leq t\leq n-1$ except for the $2$D hypercube when $t=0$, and the $k$-ary $n$-cube with odd $k\geq 5$ is not super-$\eta_{n-1}$. An algorithm is proposed to obtain a minimum embedded-edge cut for hypercubes and $k$-ary $n$-cubes with odd $k\geq 3$.
Cited by 0Open access
Vishnu Sharon, B. Karthikeyan, Sudharshan Chakravarthy et al. · 2016
Images with embedded data can be used to convey secrets using simple, fast and stand-alone novel algorithms, which when combined together, yields a more complex algorithm. This paper deals with a prime bit-XOR encryption with a recursive diagonal transformation as a pre-processing step and is then embedded using a novel 3 bits per 2 pixels Least Significant Bit (LSB) steganography into the image using the Super-knight's tour Algorithm (for texts) and Discrete Cosine Transform (DCT) based steganography (for images). This entire process is automated using Raspberry Pi in an innovative manner. The results were found to be lossless, secure and high image metric values have been achieved.
Cited by 5
Maria del Carmen MLDES, Minoru Inamura · Journal of Agricultural Meteorology · 2005
We present a practical multidimensional framework for obtaining a super-resolution image from a subpixel shifted sequence through the reduction of noise followed by a recursive back-projection algorithm. The noise-reduction stage, for thermal patterns, uses the multi-observation for identifying the fixed pattern noise. As an alternative, we present a neighborhood classification method that identifies the type and degree of the fixed noise that is subtracted from the image. In the case of radar and ultrasonic images, the multiplicative speckle noise is reduced with a filter that adaptively calculates the size of the filtering window and performs a median filter only considering the pixels with similar values inside the window. The super-resolution technique performs the downsampling of the pre-processed image sequences followed by a back-projection algorithm. Different evaluation methods demonstrate the accuracy and quality of the results. Finally, we propose a multireflecting system adapted to the camera, provided with a rotational scanning as a hardware solution for the data acquisition stage.
Cited by 0Open access
Li Lin · SHILAP Revista de lepidopterología · 2021
In recent years,deep learning has been widely used in image super-resolution reconstruction.To solve the problems of inadequate feature extraction,loss of details and gradient disappearance in super-resolution reconstruction methods based on deep learning,a deep recursive residual neural network model based on channel attention is proposed for single image super-resolution reconstruction.The proposed model constructs a simple recursive residual network structure by residual nested networks and jump connections to deepen the network and speed up its convergence while avoiding network degradation and gradient problems.An attention mechanism is introduced into the feature extraction part to improve the discriminant learning ability of the network for more accurate and more effective extraction of deep residual features,which is combined with the subsequent reconstruction network with parallel mapping structure to ensure the final accurate reconstruction.Quantitative and qualitative assessments are performed on benchmark dataset Set5,Set14,B100 and Urban100 at the magnification of 2,3 and 4 times by comparison with the mainstream methods.Experimental results show that the objective index values of the proposed method increase significantly compared to the comparative methods on all four test data sets.Among them,compared with the interpolation method and the SRCNN algorithm,the average PSNR improves 3.965dB and 1.56dB,3.19dB and 1.42dB,2.79dB and 1.32dB,respectively,at the magnification of 2,3 and 4 times.Visual effects show that the proposed method can recover image details better.
Cited by 0Open access
Jiacheng Wang, Yunmei Fang, Juntao Fei · Mathematics · 2023
Aiming at the unknown uncertainty of an active power filter system in practical operation, combining the advantages of self-feedback structure, interval type-2 fuzzy neural network, and super-twisting sliding mode, an adaptive super-twisting sliding mode control method of interval type-2 fuzzy neural network with self-feedback recursive structure (IT2FNN-SFR STSMC) is proposed in this paper. IT2FNN has an uncertain membership function, which can enhance the nonlinear ability and robustness of the network. The historical information will be stored and utilized by the self-feedback recursive structure (SFR) at runtime. Therefore, the novel IT2FNN-SFR is designed to improve the dynamic approximation effect of the neural network and reduce the dependence of the controller on the actual mathematical model. The adaptive rate of each weight of the neural network is designed by the Lyapunov method and gradient descent (GD) algorithm to ensure the convergence and stability of the system. Super-twisting sliding mode control (STSMC) has strong robustness, which can effectively reduce system chattering, and improve control accuracy and system performance. The gain of the integral term in the STSMC is set as a constant, and the other gain is changed adaptively whose adaptive rate is deduced through the stability proof of the neural network, which greatly reduces the difficulty of parameter adjustment. The harmonic suppression ability of the designed control strategy is verified by simulation experiments.
Cited by 9Open access
Wu , Shanli · Journal of Combinatorial Mathematics and Combinatorial Computing · 2025
In order to optimize the design effect of cultural and creative products with non-heritage patterns, this paper uses image reconstruction algorithm and image recognition algorithm to process non-heritage problem patterns.By combining the processed non-heritage cultural patterns with consumer demand for cultural and creative products, non-heritage cultural pattern cultural and creative products are designed to meet market demand.On the basis of recursive network, we add multi-scale feature extraction module and attention feature fusion module, choose 1 L loss function to optimize the details of image reconstruction, and construct image super-resolution reconstruction algorithm based on multi-scale recursive attention feature fusion network.And the image feature extraction network containing MSA module is designed, which is the fine-grained image recognition network based on multi-scale attention.The non-heritage cultural pattern dataset is established, and in order to optimize the recognition rate of non-heritage patterns, the image reconstruction based on multi-scale recursive attention feature fusion network is carried out on the non-heritage cultural pattern data.In view of the creative design strategy of non-heritage culture, the evaluation indexes of non-heritage cultural and creative product design are obtained from the consumer research, and the implementation suggestions of non-heritage pattern cultural and creative product design are derived based on the ranking of the importance of the evaluation indexes.The multi-scale recursive attention feature fusion network proposed in this paper achieves 34.89dB and 90.52% indicator scores on the Set5 dataset.For the design of cultural and creative products with non-heritage patterns, consumers make more suggestions in terms of functional differentiation, having a response rate of 21.58%.
Cited by 0Open access
Gavrilyuk, Ivan, Makarov, Volodymyr, Romaniuk, Nataliia · arXiv (Cornell University) · 2017
A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some homotopy considerations. As a result, the eigenvalue problem (which is in fact nonlinear) is replaced by a sequence of linear boundary value problems (besides the first one) with a singular linear operator called the exact functional discrete scheme (EFDS). A finite subsequence of $m$ terms, called truncated functional discrete scheme (TFDS), is the basis for our algorithm. The approach provides an super-exponential convergence rate as $m \to \infty$. The eigenpairs can be computed in parallel for all given indexes. The algorithm is based on some recurrence procedures including the basic arithmetical operations with the coefficients of some expansions only. This is an exact symbolic algorithm (ESA) for $m=\infty$ and a truncated symbolic algorithm (TSA) for a finite $m$. Numerical examples are presented to support the theory.
Cited by 0Open access
Anna Lanko, Nadezhda I. Nedashkovskaya · System research and information technologies · 2025
This article examines evaluation metrics for the results of super-resolution image generation in solving the SISR task. The study comprises two experiments: the implementation of custom network architectures for SRGAN, VDSR, and SRCNN, and fine-tuning of pre-trained SRGAN, VDSR, and SRCNN models. An algorithm for assessing the quality of models and deep learning methods for generating super-resolution images is suggested. The VDSR model performed best in terms of pixel, structural, and perceptual metrics, as well as training time and visual confirmation by a human, highlighting that residual learning is more effective than recursive learning under the conditions of the two conducted experiments. Threshold values for practically acceptable and high-quality results were determined through visual analysis of many generated images and their corresponding quality metrics, including those reported by other researchers.
Cited by 0Open access
Анна Ланько, Надія Іванівна Недашківська · The Scientific Issues of Ternopil Volodymyr Hnatiuk National Pedagogical University Series pedagogy · 2025
This article examines evaluation metrics for the results of super-resolution image generation in solving the SISR task. The study comprises two experiments: the implementation of custom network architectures for SRGAN, VDSR, and SRCNN, and fine-tuning of pre-trained SRGAN, VDSR, and SRCNN models. An algorithm for assessing the quality of models and deep learning methods for generating super-resolution images is suggested. The VDSR model performed best in terms of pixel, structural, and perceptual metrics, as well as training time and visual confirmation by a human, highlighting that residual learning is more effective than recursive learning under the conditions of the two conducted experiments. Threshold values for practically acceptable and high-quality results were determined through visual analysis of many generated images and their corresponding quality metrics, including those reported by other researchers.
Cited by 0Open access
Mahdi S. Hosseini, Alfred Chen, Konstantinos N. Plataniotis · arXiv (Cornell University) · 2019
Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in scientific computing including interpolation, super-resolution, and construction of special matrices applied in cryptography. Despite its numerous applications, the matrix is highly ill-conditioned where specialized treatments are considered for approximation such as conversion to Cauchy matrix, spectral decomposition, and algorithmic tailoring of the numerical solutions. In this paper, we propose a generalized algorithm that takes arbitrary pairwise (non-repetitive) sample nodes for solving inverse Vandermonde matrix. This is done in two steps: first, a highly balanced recursive algorithm is introduced with $\mathcal{O}(N)$ complexity to solve the combinatorics summation of the elementary symmetric polynomials; and second, a closed-form solution is tailored for inverse Vandermonde where the matrix' elements utilize this recursive summation for the inverse calculations. The numerical stability and accuracy of the proposed inverse method is analyzed through the spectral decomposition of the Frobenius companion matrix that associates with the corresponding Vandermonde matrix. The results show significant improvement over the state-of-the-art solutions using specific nodes such as $N$th roots of unity defined on the complex plane. A basic application in one dimensional interpolation problem is considered to demonstrate the utility of the proposed method for super-resolved signals.
Cited by 2Open access
Qiqin Dai, Seunghwan Yoo, Armin Kappeler et al. · IEEE Transactions on Image Processing · 2016
In this paper, we propose two multiple-frame super-resolution (SR) algorithms based on dictionary learning (DL) and motion estimation. First, we adopt the use of video bilevel DL, which has been used for single-frame SR. It is extended to multiple frames by using motion estimation with sub-pixel accuracy. We propose a batch and a temporally recursive multi-frame SR algorithm, which improves over single-frame SR. Finally, we propose a novel DL algorithm utilizing consecutive video frames, rather than still images or individual video frames, which further improves the performance of the video SR algorithms. Extensive experimental comparisons with the state-of-the-art SR algorithms verify the effectiveness of our proposed multiple-frame video SR approach.
Cited by 39
Song Gao, Jingying Yang, Dexin Li et al. · 2025
The decomposition performance of the IVMD method (Improved Variational Mode Decomposition) is critically determined by two key factors: the number of decomposition modes K and the penalty factor α. To ensure that the IVMD method achieves optimal decomposition results when processing signals, this paper employs the TTAO method (Triangulation Topology Aggregation Optimizer) to optimize the existing IVMD algorithm. Specifically, the optimized IVMD is used to denoise and reconstruct noisy sub-synchronous and super-synchronous oscillation signals. Subsequently, the RLS algorithm (Recursive Least Squares) is applied to identify the frequency and amplitude parameters of the reconstructed signals. Finally, the effectiveness of the method proposed in this paper is verified using ADPSS simulation examples and measured data from a new energy power station.
Cited by 0
Alvaro Lopez Paredes, Miguel Heredia Conde, Thoriq Ibrahim et al. · Zenodo (CERN European Organization for Nuclear Research) · 2023
Time-of-Flight cameras, especially the ones featuring sensors built upon macro-pixel architectures, are generally characterized by lower resolutions than other imaging modalities. In this work, we propose a practical single-frame super-resolution scheme to surpass this limitation by exploiting the architecture of a laboratory-designed macro-pixel ultra-high-speed image sensor. In addition, we propose a two-step sparsity-aware greedy algorithm for the recovery of the signal in the time (depth) domain. The main contribution of our algorithm is the introduction of a preliminary screening step to define a set of feasible support candidates in which we replace the demodulation functions, the assembly of which yields the sensing matrix, by the theoretical binary codes they are built upon. We empirically demonstrate that our algorithm improves the recovery performance with respect to Order Recursive Matching Pursuit for sparsity ≤ 2.
Cited by 0Open access
Kassem Al Ismaeil, Djamila Aouada, Thomas Solignac et al. · 2015
This paper proposes to enhance low resolution dynamic depth videos containing freely non-rigidly moving objects with a new dynamic multi-frame super-resolution algorithm. Existent methods are either limited to rigid objects, or restricted to global lateral motions discarding radial displacements. We address these shortcomings by accounting for non-rigid displacements in 3D. In addition to 2D optical flow, we estimate the depth displacement, and simultaneously correct the depth measurement by Kalman filtering. This concept is incorporated efficiently in a multi-frame super-resolution framework. It is formulated in a recursive manner that ensures an efficient deployment in real-time. Results show the overall improved performance of the proposed method as compared to alternative approaches, and specifically in handling relatively large 3D motions. Test examples range from a full moving human body to a highly dynamic facial video with varying expressions.
Cited by 10
Wei Dai, Guochu Shou, Yihong Hu et al. · 2014
Control plane, in Software-defined Networking (SDN), can configure and manage data plane in a centralized way. However, a centralized control plane introduces a problem in scaling SDN network. In terms of network virtualization, we can abstract the network layer by layer in a recursive way. As a result, the whole network can be simplified as a super switch, and it looks like that all hosts or servers are connected to the same switch. All of tasks, such as calculation of the shortest path, are implemented in this switch, and will be decomposed layer by layer. This new design of architecture is named R-SDN. We develop this recursive idea into an algorithm based on Fibonacci series. In order to validate our design, we apply this new model into scenarios of unicast and multicast. Also, we evaluate this model in different kinds of topology.
Cited by 1