Change Point Detection Using Penalized Multidegree Splines

We consider a function estimation method with change point detection using truncated power spline basis and elastic-net-type L1-norm penalty. The L1-norm penalty controls the jump detection and smoothness depending on the value of the parameter. In terms of the proposed estimators, we introduce two computational algorithms for the Lagrangian dual problem (coordinate descent algorithm) and constrained convex optimization problem (an algorithm based on quadratic programming). Subsequently, we investigate the relationship between the two algorithms and compare them. Using both simulation and real data analysis, numerical studies are conducted to validate the performance of the proposed method.

A Modified Recursive Regularization Factor Calculation for Sparse RLS Algorithm with l1-Norm

In this paper, we propose a new calculation method for the regularization factor in sparse recursive least squares (SRLS) with l1-norm penalty. The proposed regularization factor requires no prior knowledge of the actual system impulse response, and it also reduces computational complexity by about half. In the simulation, we use Mean Square Deviation (MSD) to evaluate the performance of SRLS, using the proposed regularization factor. The simulation results demonstrate that SRLS using the proposed regularization factor calculation shows a difference of less than 2 dB in MSD from SRLS, using the conventional regularization factor with a true system impulse response. Therefore, it is confirmed that the performance of the proposed method is very similar to that of the existing method, even with half the computational complexity.

Streamflow simulation in data-scarce basins using Bayesian and physics-informed machine learning models

Hydrologic predictions at rural watersheds are important but also challenging due to data shortage. Long Short-TermMemory (LSTM) networks are a promising machine learning approach and have demonstrated good performance in streamflow predictions. However, due to its data-hungry nature, most of LSTM applications focused on well-monitored catchments with abundant and high quality observations. In this work, we investigate predictive capabilities of LSTM in poorly monitored watersheds with short observation records. To address three main challenges of LSTM applications in data-scarce locations, i.e., overfitting, uncertainty quantification (UQ), and out-of-distribution prediction, we evaluate different regularization techniques to prevent overfitting, apply a Bayesian LSTM for UQ, and introduce a physics-informed hybrid LSTM to enhance out-of-distribution prediction. Through case studies in two diverse sets of catchments with and without snow influence, we demonstrate that: (1) when hydrologic variability in the prediction period is similar to the calibration period, LSTM models can reasonably predict daily streamflow with Nash-Sutcliffe efficiency above 0.8, even with only two years of calibration data. (2) When the hydrologic variability in the prediction and calibration periods is dramatically different, LSTM alone does not predict well, but the hybrid model can improve the out-of-distribution prediction with acceptable generalization accuracy. (3) L2 norm penalty and dropout can mitigate overfitting, and Bayesian and hybrid LSTM have no overfitting. (4) Bayesian LSTM provides useful uncertainty information to improve prediction understanding and credibility. These insights have vital implications for streamflow simulation in watersheds where data quality and availability are a critical issue.

Diagnosis of Benign and Malignant Renal Tumors Based on Multi-Feature Sparse Constraints

Considering that the kidneys segmentation challenge for image processing because of the gray level from abdominal computer tomography (CT) scans is a great similarity of adjacent organs, partial volume effects and so on, a novel multi-feature sparse constraints strategy is proposed to diagnose the benign and malignant renal tumors, which can improve the accuracy and reliability of segmentation. The weighted sparse measure is defined by introducing weights in the l1-norm of vectors. The weight is inversely proportional to the similarity between data, therefore the weighted l1-norm penalty on the linear representation coefficients tends to force similar data be involved while dissimilar data uninvolved in the linear representation of a datum. The resulted representation can overcome the drawbacks of l1-norm penalty that the presentation coefficients are usually over sparse and not robust for highly correlated data. Experimental results and objective assessment indexes show that the proposed method can effectively segment CT images with good visual consistency. In addition, the dice coefficients of renal and renal tumors were 0.933 and 0.854, respectively. In addition, our method can also be used for the diagnosis of renal tumors, and has also achieved good performance.

Reweighted Covariance Fitting Based on Nonconvex Schatten-p Minimization for Gridless Direction of Arrival Estimation

In this paper, we reformulate the gridless direction of arrival (DoA) estimation problem in a novel reweighted covariance fitting (CF) method. The proposed method promotes joint sparsity among different snapshots by means of nonconvex Schatten-p quasi-norm penalty. Furthermore, for more tractable and scalable optimization problem, we apply the unified surrogate for Schatten-p quasi-norm with two-factor matrix norms. Then, a locally convergent iterative reweighted minimization method is derived and solved efficiently via a semidefinite program using the optimization toolbox. Finally, numerical simulations are carried out in the background of unknown nonuniform noise and under the consideration of coprime array (CPA) structure. The results illustrate the superiority of the proposed method in terms of resolution, robustness against nonuniform noise, and correlations of sources, in addition to its applicability in a limited number of snapshots.

Decoupling strategy for large-scale multiphysics joint inversion

<p>We present a generalized 3-D multiphysics joint inversion scheme with a focus on large-scale regional problems. One of the key features of this scheme is the formulation of the structure coupling as a sparsity-promoting joint regularization. This approach makes it possible to simplify the structure of the objective function and to keep the number of hyperparameters relatively low, so that the inversion framework complexity scales well with respect to the number of geophysical methods and possible reference models used. To further simplify adding geophysical solvers to the framework and to optimize the discretization, we propose an alternating minimization scheme that decouples the inversion and the joint regularization steps. Decoupling is achieved by introducing an auxiliary multi-parameter model. This allows the individual subproblems to make use of problem-tailored grids and specialized optimization algorithms. As we will see, this is in particular important for the regularization subproblem. In contrast to straightforward 'cooperative inversion' formulation, decoupled inversion steps appear to be regularized by a standard quadratic model-norm penalty, and as a result existing separate inversion codes can be used with minimal, if any, modifications. The developed scheme is applied to magnetotelluric, seismic and gravity data and tested on synthetic model examples.</p>