A rigorous perturbation analysis is presented for the singular value decomposition (SVD) of a real matrix with full column rank. It is proved that the SVD perturbation problem is well posed only when the singular values are distinct. The analysis inv...
Singular value decomposition has recently seen a great theoretical improvement for k-tridiagonal matrices, obtaining a considerable speed up over all previous implementations, but at the cost of not ordering the singular values. We provide here a ref...
Hyers and Ulam considered the problem of whether there is a true isometry that approximates the
This paper is motivated by the need to stabilise the impact of deep learning (DL) training for medical image analysis on the conditioning of convolution filters in relation to model overfitting and robustness. We present a simple strategy to reduce s...
In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their in...
Reducing noise pollution in signals is of great significance in the field of signal detection. In order to reduce the noise in the signal and improve the signal-to-noise ratio (SNR), this paper takes the singular value decomposition theory as the sta...
The singular value decomposition package (SVDP) is often used for signal decomposition and feature extraction. At present, the general SVDP has insufficient feature extraction ability due to the two-row structure of the Hankel matrix, which leads to...
The navigation accuracy of a star sensor depends on the estimation accuracy of its optical parameters, and so, the parameters should be updated in real time to obtain the best performance. Current on-orbit calibration methods for star sensors mainly...
Nonlinear distortion in loudspeaker systems degrades sound quality and must be properly compensated for by linearization techniques. One technique to reduce nonlinear distortion is to use a Volterra Filter, which approximates the nonlinearity of the...
Singular value decomposition (SVD) is a fundamental technique widely used in various applications, such as recommendation systems and principal component analyses. In recent years, the need for privacy-preserving computations has been increasing cons...
We investigate and discuss in detail the structure of the restricted singular value decomposition for a tensor triplet under t-product (T-RSVD). The algorithm is provided with a numerical example illustrating the main result. For applications, we con...
Partial discharge detection is an important means of insulation diagnosis of electrical equipment. To effectively suppress the periodic narrowband and white noise interferences in the process of partial discharge detection, a partial discharge interf...
To enhance imaging quality, singular value decomposition (SVD) has been applied to single-wavelength ghost imaging (GI) or color GI. In this paper, we extend the application of SVD to wavelength-multiplexing ghost imaging (WMGI) for reducing the redu...
Singular value decomposition (SVD) plays a critical role in signal processing, image analysis, and particularly in MIMO channel estimation, where it enables spatial multiplexing and interference mitigation. This study presents a configurable parallel...
The traces used in side-channel analysis are essential to breaking the key of encryption and the signal quality greatly affects the correct rate of key guessing. Therefore, the preprocessing of side-channel traces plays an important role in side-chan...
Due to the inevitable acquisition system noise and strong background noise, it is often difficult to detect the features of weak signals. To solve this problem, sparse representation can effectively extract useful information according to the sparse...
An ultrasonic reverse time migration imaging method, based on high-order singular value decomposition, is proposed in the study to solve the problems of low signal-to-noise ratio (SNR) and excessive artifacts in defect ultrasonic detection imaging re...
The accuracy of time delay estimation seriously affects the accuracy of sound source localization. In order to improve the accuracy of time delay estimation under the condition of low SNR, a delay estimation optimization algorithm based on singular v...
We analyzed the relationship between the cooperative actions of golf swings and the differences in swing trajectory. To extract cooperative actions from different swings, we acquired swing data in an experiment on an experienced golfer who swung with...
As the basis for guiding business process decisions, flowcharts contain sensitive information pertaining to process-related concepts. Therefore, it is necessary to encrypt them to protect the privacy or security of stakeholders. Using the principles...
The Singular Value Decomposition (SVD) is a fundamental algorithm used to understand the structure of data by providing insight into the relationship between the row and column factors. SVD aims to approximate a rectangular data matrix, given some ra...
In this paper, we propose a compressionmethod for optical encryption using singular value decomposition (SVD). Double random phase encryption (DRPE), which employs two distinct random phase masks, is adopted as the optical encryption technique. Since...
A new algorithm based on singular value decomposition (SVD) to remove cardiac contamination from trunk electromyography (EMG) is proposed. Its performance is compared to currently available algorithms at different signal-to-noise ratios (SNRs). The a...
Recently, methods for obtaining a high spatial resolution hyperspectral image (HR-HSI) by fusing a low spatial resolution hyperspectral image (LR-HSI) and high spatial resolution multispectral image (HR-MSI) have become increasingly popular. However,...
Rotating machinery is widely used in industrial applications. With the trend towards more precise and more critical operating conditions, mechanical failures may easily occur. Condition monitoring and fault diagnosis (CMFD) technology is an effective...
We propose and demonstrate a single-pixel imaging method based on deep learning network enhanced singular value decomposition. The theoretical framework and the experimental implementation are elaborated and compared with the conventional methods bas...
In this article, we discuss possible observing strategies for a simplified ocean model (Double Gyre (DG)), used as a preliminary tool to understand the observation needs for real analysis and forecasting systems. Observations are indeed fundamental t...
The impulsive fault feature signal of rolling bearings at the early failure stage is easily contaminated by the fundamental frequency (i.e., the rotation frequency of the shaft) signal and background noise. To address this problem, this paper puts fo...
The multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) technology is the combination of the OFDM and MIMO technologies, which could improve the system capacity and make efficient utilization of the frequency spectru...
Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudoinverse of...
The problem of analyzing a big amount of user data to determine their preferences and, based on these data, to provide recommendations on new products is important. Depending on the correctness and timeliness of the recommendations, significant profi...
To extract partial discharge (PD) signals from white noise efficiently, this paper proposes a denoising method for PD signals, named adaptive short-time singular value decomposition (ASTSVD). First, a sliding window was moved along the time axis of a...
Coherent plane-wave compounding (CPWC) is widely used in medical ultrasound imaging, in which plane-waves tilted at multiple angles are used to reconstruct ultrasound images. CPWC helps to achieve a balance between frame rate and image quality. Howev...
Full control of the light field at the tip of the fiber holds the possibility of producing structured illumination patterns such as LG-beams or vector light fields, which have important applications in different fields such as imaging and quantum tec...
Singular value decomposition (SVD) is a central mathematical tool for several emerging applications in embedded systems, such as multiple-input multiple-output (MIMO) systems, data analytics, sparse representation of signals. Since SVD algorithms red...
Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singula...
In order to accurately evaluate the flow stability of the flow standard facility, the flow fluctuation in the standard facility needs to be accurately measured. However, the flow fluctuation signal is always superimposed with the fluctuation signal o...
The periodic impulse characteristics caused by rolling bearing damage are weak in the incipient failure stage. Thus, these characteristics are always drowned out by background noise and other harmonic interference. A novel approach based on multi-res...
Missing values commonly exist in dam inflow flood discharge monitoring data, which hinders flood analysis, risk assessment and reservoir scheduling. Aiming at the problems of insufficient imputation accuracy and the difficulty in adaptive threshold s...
This paper presents the results of applying the new mechanization of the Kalman filter (KF) algorithm using singular value decomposition (SVD). The proposed algorithm is useful in applications where the influence of round-off errors reduces the accur...
As optical networks evolve towards flexibility and heterogeneity, various modulation formats are used to match different bandwidth requirements and channel conditions. For correct reception and efficient compensation, modulation format identification...
Fetal electrocardiograms (FECGs) provide important clinical information for early diagnosis and intervention. However, FECG signals are extremely weak and are greatly influenced by noises. FECG signal extraction and detection are still challenging. I...
The geometric distribution of seabed beacons significantly impacts the positioning accuracy of underwater acoustic navigation systems. To address this challenge, we propose a depth-constrained adaptive stochastic model optimization method based on si...
The detection of small targets within the background of sea clutter is a significant challenge faced in radar signal processing. Small target echoes are weak in energy, and can be submerged by sea clutter and sea spikes, which are caused by overturni...
Recent efforts on the decarbonization, autonomy, and safety of the maritime vehicles required comprehensive analyses and prediction of the behavior of the existing vessels and prospective adaptations. To predict the performance of vessels, a better u...
In the weld bonding used in automobiles, inspecting the adhesive areas is important to achieve the desired increase in rigidity. Active infrared thermography using flash lamp heating was applied to a weld-bonded specimen. Temperature differences were...
For 5G and beyond cellular communication systems, new coding and modulation techniques are suggested to reach the requirements of high data rate and quality of service. In this paper, a new space-time coded orthogonal transform division multiplexing...
Recently, an increasing number of cities have deployed bicycle-sharing systems to solve the first/last mile connection problem, generating a large quantity of data. In this paper, singular value decomposition (SVD) was used to extract the main featur...
Coronary computed tomography angiography (CCTA) is widely used due to its improvements in computed tomography (CT) diagnostic performance. Unlike other CT examinations, CCTA requires shorter rotation times of the X-ray tube, improving the temporal re...
Heart rate measurement using a continuous wave Doppler radar sensor (CW-DRS) has been applied to cases where non-contact detection is required, such as the monitoring of vital signs in home healthcare. However, as a CW-DRS measures the speed of movem...
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