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The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method, we propose the so-called heavy-ball-based hard thresholding (HBHT) and heavy-ball-based hard thresholding pursuit (HBHTP) algorithms for signal recovery. It turns out that the HBHT and HBHTP can successfully recover a $k$-sparse signal if the restricted isometry constant of the measurement matrix satisfies $\delta_{3k}<0.618 $ and $\delta_{3k}<0.577,$ respectively. The guaranteed success of HBHT and HBHTP is also shown under the conditions $\delta_{2k}<0.356$ and $\delta_{2k}<0.377,$ respectively. Moreover, the finite convergence and stability of the two algorithms are also established in this paper. Simulations on random problem instances are performed to compare the performance of the proposed algorithms and several existing ones. Empirical results indicate that the HBHTP performs very comparably to a few existing algorithms and it takes less average time to achieve the signal recovery than these existing methods.

Recently, deep convolution neural networks (CNNs) steered face super-resolution methods have achieved great progress in restoring degraded facial details by jointly training with facial priors. However, these methods have some obvious limitations. On the one hand, multi-task joint learning requires additional marking on the dataset, and the introduced prior network will significantly increase the computational cost of the model. On the other hand, the limited receptive field of CNN will reduce the fidelity and naturalness of the reconstructed facial images, resulting in suboptimal reconstructed images. In this work, we propose an efficient CNN-Transformer Cooperation Network (CTCNet) for face super-resolution tasks, which uses the multi-scale connected encoder-decoder architecture as the backbone. Specifically, we first devise a novel Local-Global Feature Cooperation Module (LGCM), which is composed of a Facial Structure Attention Unit (FSAU) and a Transformer block, to promote the consistency of local facial detail and global facial structure restoration simultaneously. Then, we design an efficient Local Feature Refinement Module (LFRM) to enhance the local facial structure information. Finally, to further improve the restoration of fine facial details, we present a Multi-scale Feature Fusion Unit (MFFU) to adaptively fuse the features from different stages in the encoder procedure. Comprehensive evaluations on various datasets have assessed that the proposed CTCNet can outperform other state-of-the-art methods significantly.

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental problem in the framework of energy-based model, where the observed expert trajectories are assumed to be random samples from a probability density function defined as the exponential of the negative cost function up to a normalizing constant. The parameters of the cost function are learned by maximum likelihood via an "analysis by synthesis" scheme, which iterates (1) synthesis step: sample the synthesized trajectories from the current probability density using the Langevin dynamics via back-propagation through time, and (2) analysis step: update the model parameters based on the statistical difference between the synthesized trajectories and the observed trajectories. Given the fact that an efficient optimization algorithm is usually available for an optimal control problem, we also consider a convenient approximation of the above learning method, where we replace the sampling in the synthesis step by optimization. Moreover, to make the sampling or optimization more efficient, we propose to train the energy-based model simultaneously with a top-down trajectory generator via cooperative learning, where the trajectory generator is used to fast initialize the synthesis step of the energy-based model. We demonstrate the proposed methods on autonomous driving tasks, and show that they can learn suitable cost functions for optimal control.

The shift towards end-to-end deep learning has brought unprecedented advances in many areas of computer vision. However, deep neural networks are trained on images with resolutions that rarely exceed $1,000 \times 1,000$ pixels. The growing use of scanners that create images with extremely high resolutions (average can be $100,000 \times 100,000$ pixels) thereby presents novel challenges to the field. Most of the published methods preprocess high-resolution images into a set of smaller patches, imposing an a priori belief on the best properties of the extracted patches (magnification, field of view, location, etc.). Herein, we introduce Magnifying Networks (MagNets) as an alternative deep learning solution for gigapixel image analysis that does not rely on a preprocessing stage nor requires the processing of billions of pixels. MagNets can learn to dynamically retrieve any part of a gigapixel image, at any magnification level and field of view, in an end-to-end fashion with minimal ground truth (a single global, slide-level label). Our results on the publicly available Camelyon16 and Camelyon17 datasets corroborate to the effectiveness and efficiency of MagNets and the proposed optimization framework for whole slide image classification. Importantly, MagNets process far less patches from each slide than any of the existing approaches ($10$ to $300$ times less).

Model predictive control (MPC) has been used widely in power electronics due to its simple concept, fast dynamic response, and good reference tracking. However, it suffers from parametric uncertainties, since it directly relies on the mathematical model of the system to predict the optimal switching states to be used at the next sampling time. As a result, uncertain parameters lead to an ill-designed MPC. Thus, this paper offers a model-free control strategy on the basis of artificial neural networks (ANNs), for mitigating the effects of parameter mismatching while having a little negative impact on the inverter's performance. This method includes two related stages. First, MPC is used as an expert to control the studied converter in order to provide a dataset, while, in the second stage, the obtained dataset is utilized to train the proposed ANN. The case study herein is based on a four-level three-cell flying capacitor inverter. In this study, MATLAB/Simulink is used to simulate the performance of the proposed method, taking into account various operating conditions. Afterward, the simulation results are reported in comparison with the conventional MPC scheme, demonstrating the superior performance of the proposed control strategy in terms of robustness against parameters mismatch and low total harmonic distortion (THD), especially when changes occur in the system parameters, compared to the conventional MPC. Furthermore, the experimental validation of the proposed method is provided based on the Hardware-in-the-Loop (HIL) simulation using the C2000TM-microcontrollerLaunchPadXL TMS320F28379D kit, demonstrating the applicability of the ANN-based control strategy to be implemented on a DSP controller.

The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners, and image contrast. However, the dilemma between restoration quality and computational efficiency is an essential roadblock for high-order methods. In this paper, we propose fast multi-grid algorithms for minimizing both mean curvature and Gaussian curvature energy functionals without sacrificing the accuracy for efficiency. Unlike the existing approaches based on operator splitting and the Augmented Lagrangian method (ALM), no artificial parameters are introduced in our formulation, which guarantees the robustness of the proposed algorithm. Meanwhile, we adopt the domain decomposition method to promote parallel computing and use the fine-to-coarse structure to accelerate the convergence. Numerical experiments are presented on both image denoising and CT reconstruction problem to demonstrate the ability to recover image texture and the efficiency of the proposed method.

This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross-Pitaevskii and Kohn-Sham equation arising in computational physics and chemistry. These problems characterize critical points of energy minimization problems on the infinite-dimensional Stiefel manifold. To efficiently compute minimizers, we propose a novel Riemannian gradient descent method induced by an energy-adaptive metric. Quantified convergence of the methods is established under suitable assumptions on the underlying problem. A non-monotone line search and the inexact evaluation of Riemannian gradients substantially improve the overall efficiency of the method. Numerical experiments illustrate the performance of the method and demonstrates its competitiveness with well-established schemes.

In this work, we develop quantization and variable-length source codecs for the feedback links in linear-quadratic-Gaussian (LQG) control systems. We prove that for any fixed control performance, the approaches we propose nearly achieve lower bounds on communication cost that have been established in prior work. In particular, we refine the analysis of a classical achievability approach with an eye towards more practical details. Notably, in the prior literature the source codecs used to demonstrate the (near) achievability of these lower bounds are often implicitly assumed to be time-varying. For single-input single-output (SISO) plants, we prove that it suffices to consider time-invariant quantization and source coding. This result follows from analyzing the long-term stochastic behavior of the system's quantized measurements and reconstruction errors. To our knowledge, this time-invariant achievability result is the first in the literature.

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.