Minimum Norm Research Articles

HPETC: History Priority Enhanced Tensor Completion for Network Distance Measurement

In network distance measurement, how to estimate the whole network distance data from partially observed samples has attracted lots of attention because of its significance for network performance evaluation. Matrix completion becomes the most effective approach. However, the two-dimension matrix can only capture the spatial features in the network distance data while ignoring the temporal features. To conquer the problem, few recent studies begin to model the network distance data as a three-dimension tensor and propose tensor completion approaches for distance estimation. Although promising, existing tensor completion approaches still suffer the problem of low recovery accuracy and high measurement cost because they ignore the history priority information. To fully utilize both spatial and temporal features hidden in the distance data, this paper formulates a novel History Priority Enhanced Tensor Completion (HPETC) for distance estimation as a weighted tensor nuclear norm minimization problem where the weight is defined based on the history subspaces information. To solve the weighted tensor nuclear norm minimization problem, we firstly transform it into a factorization-based Frobenius norm minimization problem to avoid costly T-SVD computations, and then propose an iterative algorithm to solve the transformed problem. We further derive a theoretical sampling bound that is lower than the existing sampling bound, thus leads a lower measurement cost. We demonstrate the effectiveness of the proposed algorithm by conducting extensive experiments using two real network distance datasets. The result shows that the proposed algorithm can not only improve the estimation accuracy but also reduce the sampling complexity compared to the state-of-the-art approaches.

Adaptive continuation based smooth -norm approximation for compressed sensing MR image reconstruction.

There are a number of algorithms for smooth -norm (SL0) approximation. In most of the cases, sparsity level of the reconstructed signal is controlled by using a decreasing sequence of the modulation parameter values. However, predefined decreasing sequences of the modulation parameter values cannot produce optimal sparsity or best reconstruction performance, because the best choice of the parameter values is often data-dependent and dynamically changes in each iteration. We propose an adaptive compressed sensing magnetic resonance image reconstruction using the SL0 approximation method. The SL0 approach typically involves one-step gradient descent of the SL0 approximating function parameterized with a modulation parameter, followed by a projection step onto the feasible solution set. Since the best choice of the parameter values is often data-dependent and dynamically changes in each iteration, it is preferable to adaptively control the rate of decrease of the parameter values. In order to achieve this, we solve two subproblems in an alternating manner. One is a sparse regularization-based subproblem, which is solved with a precomputed value of the parameter, and the second subproblem is the estimation of the parameter itself using a root finding technique. The advantage of this approach in terms of speed and accuracy is illustrated using a compressed sensing magnetic resonance image reconstruction problem and compared with constant scale factor continuation based SL0-norm and adaptive continuation based -norm minimization approaches. The proposed adaptive estimation is found to be at least twofold faster than automated parameter estimation based iterative shrinkage-thresholding algorithm in terms of CPU time, on an average improvement of reconstruction performance 15% in terms of normalized mean squared error. An adaptive continuation-based SL0 algorithm is presented, with a potential application to compressed sensing (CS)-based MR image reconstruction. It is a data-dependent adaptive continuation method and eliminates the problem of searching for appropriate constant scale factor values to be used in the CS reconstruction of different types of MRI data.

Determinants of Food Security Status of Agricultural Households: An Empirical Investigation from Kuttanad Wetland System in Kerala, India

Recent debates highlight that agriculture-based strategies can enhance food security. Thus, this article examined the incidence and determinants of food security of agricultural households in Kuttanad, a wetland region situated in the southern part of the state of Kerala in India. Towards this objective, we have collected food consumption data from households and converted them into an equivalent amount of calorie intake. Further, we define food security in terms of calorie adequacy using the minimum calorie norm of 1,800 kcal suggested by the Food and Agricultural Organization for India. Our empirical results reveal that 37% of the sample households are food insecure. The incidence of food insecurity is higher among poor sections like labour households, Antyodaya Anna Yojana (AAY), and Scheduled Castes families. Results of Probit regression show that below poverty line and AAY families are less likely to be food secure than above poverty line families. The purchase of cereals from the Public Distribution System is found to have a positive impact on the food security status of the households. Both farm income and non-farm income positively influence the probability of food security. The study concludes that there are impediments to realizing the linkages between agriculture and food security. JEL Classification: Q10, Q18, I32, C25

Iterative algorithm to the generalized coupled Sylvester‐transpose matrix equations with application in robust and minimum norm observer design of linear systems

AbstractThis article consider a class of generalized coupled Sylvester‐transpose matrix equations which play an important role in control and systems theory. Based on the Jacobi iterative algorithm, the full‐row rank accelerated Jacobi gradient based iterative (RRAJGI) algorithm and the full‐column rank accelerated Jacobi gradient based iterative (CRAJGI) algorithm are proposed. By using the Frobenius norm of matrix and the trace function of matrix, the convergence of the algorithms are proved. The results show that the new algorithms are convergent for arbitrary initial matrices under the convergence number satisfies appropriate conditions. Numerical examples show that RRAJGI algorithm and CRAJGI algorithm have the advantages of faster convergence speed and higher convergence accuracy than other existing algorithms. Finally, an application example for robust and minimum norm observer design of linear systems is given.

Enhanced Moving Source Localization with Time and Frequency Difference of Arrival: Motion-Assisted Method for Sub-Dimensional Sensor Networks

Localizing a moving source by Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) commonly requires at least N+1 sensors in N-dimensional space to obtain more than N pairs of TDOAs and FDOAs, thereby establishing more than 2N equations to solve for 2N unknowns. However, if there are insufficient sensors, the localization problem will become underdetermined, leading to non-unique solutions or inaccuracies in the minimum norm solution. This paper proposes a localization method using TDOAs and FDOAs while incorporating the motion model. The motion between the source and sensors increases the equivalent length of the baseline, thereby improving observability even when using the minimum number of sensors. The problem is formulated as a Maximum Likelihood Estimation (MLE) and solved through Gauss–Newton (GN) iteration. Since GN requires an initialization close to the true value, the MLE is transformed into a semidefinite programming problem using Semidefinite Relaxation (SDR) technology, while SDR results in a suboptimal estimate, it is sufficient as an initialization to guarantee the convergence of GN iteration. The proposed method is analytically shown to reach the Cramér–Rao Lower Bound (CRLB) accuracy under mild noise conditions. Simulation results confirm that it achieves CRLB-level performance when the number of sensors is lower than N+1, thereby corroborating the theoretical analysis.

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

Sparse linear array synthesis using artificial neural network and nonconvex optimization

AbstractThe concept of sparse array synthesis has attracted considerable attention due to its potential to reduce hardware costs in array design and enhance the efficiency of array aperture utilization. In contrast to conventional artificial neural networks (ANNs), a more efficient encoder–decoding ANN framework is proposed in this letter for designing sparse linear arrays. The decoder is pretrained with a randomly generated training set, enabling its ability to rapidly predictiction of far‐field patterns. This process considers the actual coupling effect among the antenna elements. The output of the encoder is used as the input of the decoder to synthesize the sparse arrays by providing the desired pattern to the encoder. During the training process, a novel ‐norm minimization nonconvex optimization method is integrated into the proposed framework to reduce the number of activated elements. The effectiveness and efficiency of the method are demonstrated through numerical and full‐wave simulations for synthesizing various linear sparse arrays, including large‐scale arrays. In comparison to existing algorithms, our proposed method exhibits superior computational efficiency and predicted accuracy with fewer elements.

Validity of the Groningen Effort Test in patients with suspected chronic solvent-induced encephalopathy.

The use of performance validity tests (PVTs) in a neuropsychological assessment to determine indications of invalid performance has been a common practice for over a decade. Most PVTs are memory-based; therefore, the Groningen Effort Test (GET), a non-memory-based PVT, has been developed. This study aimed to validate the GET in patients with suspected chronic solvent-induced encephalopathy (CSE) using the criterion standard of 2PVTs. A second goal was to determine diagnostic accuracy for GET. Sixty patients with suspected CSE referred for NPA were included. The GET was compared to the criterion standard of 2PVTs based on the Test of Memory Malingering and the Amsterdam Short Term Memory Test. The frequency of invalid performance using the GET was significantly higher compared to the criterion of 2PVTs (51.7% vs. 20.0% respectively; p < 0.001). For the GET index, the sensitivity was 75% and the specificity was 54%, with a Youden's Index of 27. The GET showed significantly more invalid performance compared to the 2PVTs criterion suggesting a high number of false positives. The general accepted minimum norm of specificity for PVTs of >90% was not met. Therefore, the GET is of limited use in clinical practice with suspected CSE patients.

One-Bit DoA Estimation for Deterministic Signals Based on -Norm Minimization

One-Bit DoA Estimation for Deterministic Signals Based on -Norm Minimization

Conditioning of random Fourier feature matrices: double descent and generalization error

Abstract We provide high-probability bounds on the condition number of random feature matrices. In particular, we show that if the complexity ratio $N/m$, where $N$ is the number of neurons and $m$ is the number of data samples, scales like $\log ^{-1}(N)$ or $\log (m)$, then the random feature matrix is well-conditioned. This result holds without the need of regularization and relies on establishing various concentration bounds between dependent components of the random feature matrix. Additionally, we derive bounds on the restricted isometry constant of the random feature matrix. We also derive an upper bound for the risk associated with regression problems using a random feature matrix. This upper bound exhibits the double descent phenomenon and indicates that this is an effect of the double descent behaviour of the condition number. The risk bounds include the underparameterized setting using the least squares problem and the overparameterized setting where using either the minimum norm interpolation problem or a sparse regression problem. For the noiseless least squares or sparse regression cases, we show that the risk decreases as $m$ and $N$ increase. The risk bound matches the optimal scaling in the literature and the constants in our results are explicit and independent of the dimension of the data.

On the Polyak momentum variants of the greedy deterministic single and multiple row‐action methods

AbstractFor solving a consistent system of linear equations, the classical row‐action method, such as Kaczmarz method, is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy‐ball momentum acceleration technique, we propose two deterministic row‐action methods and establish the corresponding convergence theory. We show that our algorithm can linearly converge to a least‐squares solution with minimum Euclidean norm. Several numerical studies have been presented to corroborate our theoretical findings. Real‐world applications, such as data fitting in computer‐aided geometry design, are also presented for illustrative purposes.

Modulation of DBS-induced cortical responses and movement by the directionality and magnitude of current administered

Subthalamic deep brain stimulation (STN-DBS) is an effective therapy for alleviating motor symptoms in people with Parkinson’s disease (PwP), although some may not receive optimal clinical benefits. One potential mechanism of STN-DBS involves antidromic activation of the hyperdirect pathway (HDP), thus suppressing cortical beta synchrony to improve motor function, albeit the precise mechanisms underlying optimal DBS parameters are not well understood. To address this, 18 PwP with STN-DBS completed a 2 Hz monopolar stimulation of the left STN during MEG. MEG data were imaged in the time-frequency domain using minimum norm estimation. Peak vertex time series data were extracted to interrogate the directional specificity and magnitude of DBS current on evoked and induced cortical responses and accelerometer metrics of finger tapping using linear mixed-effects models and mediation analyses. We observed increases in evoked responses (HDP ~ 3–10 ms) and synchronization of beta oscillatory power (14–30 Hz, 10–100 ms) following DBS pulse onset in the primary sensorimotor cortex (SM1), supplementary motor area (SMA) and middle frontal gyrus (MFG) ipsilateral to the site of stimulation. DBS parameters significantly modulated neural and behavioral outcomes, with clinically effective contacts eliciting significant increases in medium-latency evoked responses, reductions in induced SM1 beta power, and better movement profiles compared to suboptimal contacts, often regardless of the magnitude of current applied. Finally, HDP-related improvements in motor function were mediated by the degree of SM1 beta suppression in a setting-dependent manner. Together, these data suggest that DBS-evoked brain-behavior dynamics are influenced by the level of beta power in key hubs of the basal ganglia-cortical loop, and this effect is exacerbated by the clinical efficacy of DBS parameters. Such data provides novel mechanistic and clinical insight, which may prove useful for characterizing DBS programming strategies to optimize motor symptom improvement in the future.

A deterministic descriptive regularization-based method for SAR tomography in urban areas

ABSTRACT In recent years, Synthetic Aperture Radar (SAR) Tomography (TomoSAR) has ascertained great potential for the three-dimensional (3-D) reconstruction of observed scenes, especially in urban areas. However, the number of proceed snapshots (observations) is usually less than that of slant height samples (unknowns) in TomoSAR inversion processes. This impairs the quality of the reconstructed vertical information. To cope with this issue and improve the reliability of reconstructed vertical information, this paper investigates the possible potential of a deterministic descriptive regularization-based method. Deterministic descriptive regularization is a well-conditioned optimization framework based on the descriptive idea of a regularization solution. This strategy can help to mitigate the effect of the ill-posed problem. Thus, it can assist SAR tomography to deal with the possible impairing issues arising from low numbers and the distribution of baselines. For this purpose, the result of the proposed strategy is compared with the outcomes from the standard TomoSAR techniques, including Beamforming, Capon, and Minimum Norm. The proposed method for reconstruction of the reflectivity function of the observed scene has been performed on a dataset acquired by the Sentinel-1 sensor in 2022 over Tehran City, Iran. The experimental results indicate that the proposed algorithm can estimate building heights with a vertical accuracy of better than 91%. These results demonstrate the great potential of the proposed method for reconstructing the full 3-D images of urban areas.

Creatinine as a predictor of muscle mass deficiency in patients with severe cerebral palsy

Energy processes in muscles can be reflected by the creatine phosphokinase system of ATP resynthesis from ADP and creatine phosphate. The product of non-enzymatic degradation of creatine (creatine phosphate) is creatinine, which accumulates in the blood serum, and its concentration correlates with the volume of the patient’s muscle tissue, subject to the normal functioning of the kidneys. Purpose. To assess the perioperative serum creatinine level as a biological marker of muscle mass in patients with severe forms of cerebral palsy, IV–V level according to GMFCS, during orthopedic interventions on the hip joint. Material and methods. A prospective clinical observational study included 82 patients with severe forms of cerebral palsy, spastic dislocations (subluxations) of the hips, for which reconstructive or palliative interventions were performed on the hip joints. The trophological status of children was assessed before surgery, the level of serum creatinine was determined in the intraoperative period, on the first postoperative day, and on the fifth day after surgery. Results. The circumference of the middle third of the shoulder in 28 % of patients, as well as the thickness of the skin-fat fold over the triceps in 61 % of children were below the 10th centile, which was regarded as malnutrition. The calculated proportion of body fat equal to 10 [8; 20] % in combination with the circumference of the muscles of the middle third of the shoulder suggest a combination of protein-energy deficiency and muscle mass deficiency in 1/5 of the patients. Creatinine indicators at all stages of observation corresponded to the minimum age norm or were below these values, tended to decrease and had a random agreement (W = 0,129). Conclusion. The level of creatinine in the blood serum correlates with the «shoulder muscle circumference» parameter in children with severe forms of cerebral palsy, severe movement disorders of IV–V level according to GMFCS. Plasma creatinine can be used as a biological marker of skeletal muscle mass in patients with severe cerebral palsy.

The WIPI Model Based on Multi-Scale Local Contrast Post-Processing for Infrared Small Target Detection

According to the infrared patch image (IPI) model theory, the infrared image background has a low rank and the target is sparse. The low-rank model can be used to separate the background and identify the target. However, in a noisy environment, the recognition effect will be affected. The higher the noise, the harder it would be to detect a small target. The residual strong fault and background edges could reduce the detection rate and increase false alarms. The traditional IPI model is adaptable to the background with the lower noise. This paper combines weighted nuclear norm minimization (WNNM) optimization with sparse representation based on the local IPI model. The background details are described more prominently by improving the nuclear norm weighting factor. The target is much easier to detect under the specific bright clouds and ground buildings background with high noise. At the same time, post-processing with image local contrast analysis is performed to compare traditional spatial filtering and local infrared patch image model algorithms. Our method has a good suppression effect on complex noise backgrounds and achieves a higher signal to clutter ratio gain (SCRG). It could also improve the target detection rate and reduce false alarms.

Semi-Proximal ADMM for Primal and Dual Robust Low-Rank Matrix Restoration from Corrupted Observations

The matrix nuclear norm minimization problem has been extensively researched in recent years due to its widespread applications in control design, signal and image restoration, machine learning, big data problems, and more. One popular model is nuclear norm minimization with the l2-norm fidelity term, but it is only effective for those problems with Gaussian noise. A nuclear norm minimization problem with the l1-norm fidelity term has been studied in this paper, which can deal with the problems with not only non-Gaussian noise but also Gaussian noise or their mixture. Moreover, it also keeps the efficiency for the noiseless case. Given the nonsmooth proposed model, we transform it into a separated form by introducing an auxiliary variable and solve it by the semi-proximal alternating direction method of multipliers (sPADMM). Furthermore, we first attempt to solve its dual problem by sPADMM. Then, the convergence guarantees for the aforementioned algorithms are given. Finally, some numerical studies are dedicated to show the robustness of the proposed model and the effectiveness of the presented algorithms.

Aerial RIS-Assisted Direction Finding Under Doppler Effect Based on Atomic Norm Minimization

Aerial RIS-Assisted Direction Finding Under Doppler Effect Based on Atomic Norm Minimization

Sparse optimization over polyhedral sets based on weighted ℓ-norm minimization

Finding the sparsest solutions over a polyhedral set is a challenging problem that has received a great deal of attention in the research community. This problem is typically NP-hard owing to the non-convexity and non-continuity of the ℓ 0 -norm. In this study, it is demonstrated that any solution of ℓ 0 -minimization over a polyhedral set must be one of the ‘extreme efficient solutions’ (EESs) of a special multiobjective optimization problem. Moreover, a new weighted ℓ 1 -norm minimization method using the Goldman–Tucker Theorem for linear optimization problems is established. Some essential features of this algorithm are examined, and numerical tests are performed to illustrate the efficiency of the proposed strategy. The numerical performance of the proposed method is compared with conventional reweighted ℓ 1 -algorithms and several compressed sensing solvers. Additionally, the method is applied to address the compressed sensing problem in magnetic resonance imaging (MRI) reconstruction.

Extreme Few-View Tomography without Training Data.

There are fewer than 10 projection views in extreme few-view tomography. The state-of-the-art methods to reconstruct images with few-view data are compressed sensing based. Compressed sensing relies on a sparsification transformation and total variation (TV) norm minimization. However, for the extreme few-view tomography, the compressed sensing methods are not powerful enough. This paper seeks additional information as extra constraints so that extreme few-view tomography becomes possible. In transmission tomography, we roughly know the linear attenuation coefficients of the objects to be imaged. We can use these values as extra constraints. Computer simulations show that these extra constraints are helpful and improve the reconstruction quality.

Efficient 2D DOA Estimation via Decoupled Projected Atomic Norm Minimization

This paper presents an efficient two-dimensional (2D) direction of arrival (DOA) estimation method, termed as decoupled projected atomic norm minimization (D-PANM), to solve the angle-ambiguity problem. It first introduces a novel atomic metric via projecting the original atom set onto a smoothing space, based on which we formulate an equivalent semi-definite programming (SDP) problem. Then, two relatively low-complexity decoupled Toeplitz matrices can be obtained to estimate the DOAs. We further exploit the structural information hidden in the newly constructed data to avoid pair matching for the azimuth and elevation angles when the number of sensors is odd, and then propose a fast and feasible decoupled alternating projections (D-AP) algorithm, reducing computational complexity to a great extent. Numerical simulations are performed to demonstrate that the proposed algorithm is no longer restricted by angle ambiguity scenarios, but instead provides a more stable estimation performance, even when multiple signals share the same angles in both azimuth and elevation dimensions. Additionally, it greatly improves the resolution, with control of the computation load compared with the existing atomic norm minimization (ANM) algorithm.