L1-norm Criterion Research Articles

Filter collaborative contribution pruning method based on the importance of different-scale layers for surface defect detection

Surface defect detection is crucial in the industrial domain, but deploying deep learning models on edge devices faces challenges of memory constraints and real-time requirements. Therefore, model pruning is necessary to reduce the model’s parameter count and improve inference speed. Due to the high detection accuracy demanded in industrial defect detection, it is essential to prune the network while ensuring minimal impact on network accuracy. Different industrial defect scenarios may exhibit defects with varying importance of features and scale representation. Hence, to preserve the network’s capability to recognize various defect features, pruning methods need to be adaptive to the dataset and effectively balance the remaining feature information across different scale layers in various scene contexts. To tackle these challenges, we propose a structured pruning method tailored for industrial detection scenarios, which significantly reduces model computation and parameter count while preserving network accuracy. Specifically, we design a scoring network to guide the allocation of pruning amounts for each layer. This network evaluates the importance of different scale layers globally based on the performance of various defect features within the dataset. Additionally, we employ the L1 norm criterion to prune filters with low weights that minimally affect accuracy. We also consider filter correlation and introduce a comprehensive evaluation method that incorporates both filter contribution and substitutability. This enables pruning of filters with low impact on detection accuracy. Finally, we obtain the most lightweight network through an iterative “prune-retraining” process. Our method is evaluated on four datasets using segmentation networks, achieving over 80% reduction in floating-point operations and 90% reduction in parameters while maintaining accuracy, thus significantly improving model memory usage and inference speed.

Robust filtering of ghost and peg-leg from sea floor seismic data

ABSTRACT. The processing of compressional waves from the acoustic components of ocean bottom seismic data is performed decomposing the compressional wavefield on its upgoing an downgoing components, treating the first order multiples, composed by the overlap between the receiver ghost and peg-leg. The separation of these wavefields is achieved through the adaptive summation of the hydrophone and geophone components, usually on a least square sense. This method of separation is known as PZ summation, because it involves an operation between pressure and vertical particle velocity measurements. However, due to the difference in response of the pressure and velocity sensors, the premises assumed on the least square summation can be violated, degrading the results. To overcome these difficulties, a more robust method can be achieved using the L1 norm criterion for the adaptive sum. A comparison was made between the results obtained with the Iterative Reweighted Least Squares and Wiener-Levinson filters. The robustness of the L1 norm sum was demonstrated by applications on PZ summation of Ocean Bottom Cable data from the Jubarte area, in the Campos Basin, Brazil, showing improvements, especially when the multiples are present in the estimation window used to derive the filter coefficients.

Rapid Detection of Small Faults and Oscillations in Synchronous Generator Systems Using GMDH Neural Networks and High-Gain Observers

This paper presents a robust and efficient fault detection and diagnosis framework for handling small faults and oscillations in synchronous generator (SG) systems. The proposed framework utilizes the Brunovsky form representation of nonlinear systems to mathematically formulate the fault detection problem. A differential flatness model of SG systems is provided to meet the conditions of the Brunovsky form representation. A combination of high-gain observer and group method of data handling neural network is employed to estimate the trajectory of the system and to learn/approximate the fault- and uncertainty-associated functions. The fault detection mechanism is developed based on the output residual generation and monitoring so that any unfavorable oscillation and/or fault occurrence can be detected rapidly. Accordingly, an average L1-norm criterion is proposed for rapid decision making in faulty situations. The performance of the proposed framework is investigated for two benchmark scenarios which are actuation fault and fault impact on system dynamics. The simulation results demonstrate the capacity and effectiveness of the proposed solution for rapid fault detection and diagnosis in SG systems in practice, and thus enhancing service maintenance, protection, and life cycle of SGs.

Decision regions and decision boundaries of generalized K mean algorithm based on various norm criteria

This paper derives the decision regions and the decision boundaries of the generalized K mean algorithms based on the L1 norm criterion, the L2 norm criterion and the L∞ norm criterion. The decision boundaries of these three generalized K mean algorithms are all linear hyperplanes. However, the total numbers of the decision boundaries of the generalized K mean algorithms based on both the L1 norm criterion and the L∞ norm criterion are more than that based on the L2 norm criterion. On the other hand, the decision regions of the generalized K mean algorithm based on the L2 norm criterion are convex while that based on both the L1 norm criterion and the L∞ norm criterion are in general nonconvex. The computer numerical simulations on a toy example demonstrate the above phenomena. Besides, two examples are illustrated. The first example on the patent image retrieval system shows that the recognition accuracies of using the generalized K mean algorithms based on the L2 norm criterion, the L1 norm criterion and the L∞ norm criterion are 58.25%, 61% and 58.75%, respectively. The second example on the electromyogram based Parkinson’s disease detection system shows that the recognition accuracies of using the generalized K mean algorithms based on the L2 norm criterion, the L1 norm criterion and the L∞ norm criterion are 60%, 60% and 67%, respectively, if the signals are classified directly in the time domain. On the other hand, the recognition accuracies of the generalized K mean algorithms based on the L2 norm criterion, the L1 norm criterion and the L∞ norm criterion are 60%, 87% and 60%, respectively, if the signals are classified directly in the discrete cosine transform domain. The improvements are due to the nonconvexity of the decision regions of the generalized K mean algorithm based on the L1 norm criterion and the L∞ norm criterion.

L1‎‎ Norm Based Data Analysis and Related Methods

This paper gives a rather general view on the L1‎‎ norm criterion on the area of data analysis and related topics. We tried to cover all aspects of mathematical properties, historical development, computational algorithms, simultaneous equations estimation, statistical modeling, and application of the L1‎‎ norm in different fields of sciences.

2DRLPP: Robust two-dimensional locality preserving projection with regularization

The recently proposed two-dimensional locality preserving projection (2DLPP) is an excellent matrix-based dimensionality reduction method. However, the formulation of 2DLPP may encounter several drawbacks in real-world applications, such as sensitiveness to outliers, non-orthogonal projections, and singularity problem. To alleviate these issues, in this paper, we propose a novel robust two-dimensional locality preserving projection (2DRLPP) for noisy image recognition. The proposed 2DRLPP preserves the local manifold structure of two-dimensional image space under the robust L1-norm criterion. Different from the existing 2DLPP, our 2DRLPP enjoys several incomparable advantages: (i) 2DRLPP extracts projections from matrix-based image space via the L1-norm locality preserving criterion rather than the L2-norm one, and hence it is more robust to outliers. (ii) The orthogonality constraint is further imposed on 2DRLPP to ensure its orthogonal projections. (iii) The introduced regularization term can not only control the model complexity but also guarantee the stability of solution. (iv) A simple but efficient iterative algorithm is presented to solve the corresponding L1-norm minimization problem, whose convergence is guaranteed theoretically. Extensive experimental results on three noisy face image datasets confirm the feasibility and robustness of the proposed approach.

On the Link Between L1-PCA and ICA.

Principal component analysis (PCA) based on L1-norm maximization is an emerging technique that has drawn growing interest in the signal processing and machine learning research communities, especially due to its robustness to outliers. The present work proves that L1-norm PCA can perform independent component analysis (ICA) under the whitening assumption. However, when the source probability distributions fulfil certain conditions, the L1-norm criterion needs to be minimized rather than maximized, which can be accomplished by simple modifications on existing optimal algorithms for L1-PCA. If the sources have symmetric distributions, we show in addition that L1-PCA is linked to kurtosis optimization. A number of numerical experiments illustrate the theoretical results and analyze the comparative performance of different algorithms for ICA via L1-PCA. Although our analysis is asymptotic in the sample size, this equivalence opens interesting new perspectives for performing ICA using optimal algorithms for L1-PCA with guaranteed global convergence while inheriting the increased robustness to outliers of the L1-norm criterion.

Low sidelobe robust imaging in random frequency-hopping wideband radar based on compressed sensing

High resolution range imaging with correlation processing suffers from high sidelobe pedestal in random frequency-hopping wideband radar. After the factors which affect the sidelobe pedestal being analyzed, a compressed sensing based algorithm for high resolution range imaging and a new minimized l 1-norm criterion for motion compensation are proposed. The random hopping of the transmitted carrier frequency is converted to restricted isometry property of the observing matrix. Then practical problems of imaging model solution and signal parameter design are resolved. Due to the particularity of the proposed algorithm, two new indicators of range profile, i.e., average signal to sidelobe ratio and local similarity, are defined. The chamber measured data are adopted to testify the validity of the proposed algorithm, and simulations are performed to analyze the precision of velocity measurement as well as the performance of motion compensation. The simulation results show that the proposed algorithm has such advantages as high precision velocity measurement, low sidelobe and short period imaging, which ensure robust imaging for moving targets when signal-to-noise ratio is above 10 dB.

Nonlinear Model Selection—Application to an Indirect Inductive Measurement of Conductivity

An efficient method and algorithm for experimental data processing based on parametric inversion is proposed. This method is applied to a metallic rod conductivity measurement based on induced secondary voltage technique. First, the case of an ideal excitation circuit is studied. For this case, when the excitation signal is a current step, a model of the data can be obtained in a closed-form as an infinite sum of exponential functions whose relaxation times are related to the physical properties of the inspected material. Therefore, for time points greater than the largest relaxation constant, only one term is sufficient; but, for these times, the signal-to-noise ratio (SNR) is smaller, so the variance of the estimated conductivity is larger. When taking into account some data at earlier time points, N terms are necessary to minimize the residual modelling error. The conductivity variance is then smaller but the identification process is more complex. A tradeoff has been achieved between these two aspects. Finally, the choice of an L1 norm criterion upon the identification error is used to reject outliers from experimental data. Second, a more realistic circuit is considered (the primary time constant is taken into account). In that case, two steps are necessary to calculate the direct model. A nonlinear equation is solved and the results are put into a closed-form expression (an infinite sum of exponential functions). For both cases, a multiparameters inversion is eventually used to minimize the effect of the modifying quantities

Tomographic inversions for mantle P wave velocity structure based on the minimization of l2 and l1 norms of International Seismological Centre Travel Time Residuals

We use International Seismological Centre (ISC) P arrival data (1964–1987) and iterative algorithms which minimize the l1 and l2 residual norms to solve simultaneously for three‐dimensional P velocity variations in Earth's mantle, source mislocations, and station corrections. We find that the maximum velocity perturbations produced by the l1 minimization (approximately ±4% in our final model) are relatively insensitive to smoothing and damping constraints. Therefore, using an l1 norm criterion allows us to keep the bias introduced to the inversion to a minimum. Among the well‐resolved features contained in both the l1 and the l2 velocity models are a fast anomaly in the lower mantle beneath the Tonga‐New Hebrides subduction zone to a depth of 1670 km and another fast anomaly beneath the Japanese island arc and eastern Asia. Continuity between these anomalies and shallower fast anomalies is not clear. A fast anomaly extending from 670 km to 2070 km depth appears beneath eastern North America, the Caribbean, and north central South America. A broad, fast anomaly appears beneath eastern Asia just above the core‐mantle boundary as well as several slow anomalies under the Pacific basin of comparable size. Both models contain a circum‐Pacific ring of 2% lower velocities in the depth range 0–200 km, associated with back arc basins. High velocities (over 2%) associated with the continental shields tend to disappear below 400 km, though a significant region of high velocity remains beneath the Siberian platform in the 400 to 670 km depth interval.

Deconvolution of marine seismic data using the l1 norm

Summary The trace measured in a marine seismic experiment can be expressed as the convolution of a source wavelet and a sparsely populated spike train which represents the impulse response of the medium. Deconvolution processing using the l1 norm criterion has been suggested by Taylor, Banks and McCoy to obtain estimates of the impulse response from noisy traces. This criterion is well-suited to problems where a spiky output is expected. In this paper we present a new l1 formulation of the deconvolution problem which represents a significant improvement over the concept proposed by Taylor et al. The performance has been tested with synthetic data where noise has been added both to the trace and the source wavelet, and the results of these trials are described. An example is presented which demonstrates the success of this method in removing bubble pulse interference from a bottom-reflected acoustic signal.