Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in various imag
e and video processing tasks. However, classical methods learn the dictionary and the sparse code based on alternating optimizations, usually without theoretical guarantees for either optimality or convergence due to non-convexity of the problem. Recent works on sparse coding with a complete dictionary provide strong theoretical guarantees thanks to the development of the non-convex optimization. However, initial non-convex approaches learn the dictionary in the sparse coding problem sequentially in an atom-by-atom manner, which leads to a long execution time. More recent works seek to directly learn the entire dictionary at once, which substantially reduces the execution time. However, the associated recovery performance is degraded with a finite number of data samples. In this paper, we propose an efficient sparse coding scheme with a two-stage optimization. The proposed scheme leverages the global and local Riemannian geometry of the two-stage optimization problem and facilitates fast implementation for superb dictionary recovery performance by a finite number of samples without atom-by-atom calculation. We further prove that, with high probability, the proposed scheme can exactly recover any atom in the target dictionary with a finite number of samples if it is adopted to recover one atom of the dictionary. An application on wireless sensor data compression is also proposed. Experiments on both synthetic and real-world data verify the efficiency and effectiveness of the proposed scheme.
We consider the optimal control of linear systems over wireless MIMO fading channels, where the MIMO wireless fading and random access of the remote controller may cause intermittent controllability or uncontrollability of the closed-loop control sys
tem. We formulate the optimal control design over random access MIMO fading channels as an infinite horizon average cost Markov decision process (MDP), and we propose a novel state reduction technique such that the optimality condition is transformed into a time-invariant reduced-state Bellman optimality equation. We provide the closed-form characterizations on the existence and uniqueness of the optimal control solution via analyzing the reduced-state Bellman optimality equation. Specifically, in the case that the closed-loop system is almost surely controllable, we show that the optimal control solution always exists and is unique. In the case that MIMO fading channels and the random access of the remote controller destroy the closed-loop controllability, we propose a novel controllable and uncontrollable positive semidefinite (PSD) cone decomposition induced by the singular value decomposition (SVD) of the MIMO fading channel contaminated control input matrix. Based on the decomposed fine-grained reduced-state Bellman optimality equation, we further propose a closed-form sufficient condition for both the existence and the uniqueness of the optimal control solution. The closed-form sufficient condition reveals the fact that the optimal control action may still exist even if the closed-loop system suffers from intermittent controllability or almost sure uncontrollability.
Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works of dictionary learning are in an offline manner. There are mainly two offline ways for dictionary learning. One is to do
an alternative optimization of both the dictionary and the sparse code; the other way is to optimize the dictionary by restricting it over the orthogonal group. The latter one is called orthogonal dictionary learning which has a lower complexity implementation, hence, it is more favorable for lowcost devices. However, existing schemes on orthogonal dictionary learning only work with batch data and can not be implemented online, which is not applicable for real-time applications. This paper proposes a novel online orthogonal dictionary scheme to dynamically learn the dictionary from streaming data without storing the historical data. The proposed scheme includes a novel problem formulation and an efficient online algorithm design with convergence analysis. In the problem formulation, we relax the orthogonal constraint to enable an efficient online algorithm. In the algorithm design, we propose a new Frank-Wolfe-based online algorithm with a convergence rate of O(ln t/t^(1/4)). The convergence rate in terms of key system parameters is also derived. Experiments with synthetic data and real-world sensor readings demonstrate the effectiveness and efficiency of the proposed online orthogonal dictionary learning scheme.
The propagation of acoustic or elastic waves in artificial crystals, including the case of phononic and sonic crystals, is inherently anisotropic. As is known from the theory of periodic composites, anisotropy is directly dictated by the space group
of the unit cell of the crystal and the rank of the elastic tensor. Here, we examine effective velocities in the long wavelength limit of periodic acoustic and elastic composites as a function of the direction of propagation. We derive explicit and efficient formulas for estimating the effective velocity surfaces, based on second-order perturbation theory, generalizing the Christofell equation for elastic waves in solids. We identify strongly anisotropic sonic crystals for scalar acoustic waves and strongly anisotropic phononic crystals for vector elastic waves. Furthermore, we observe that under specific conditions, quasi-longitudinal waves can be made much slower than shear waves propagating in the same direction.
Wireless backhaul is considered to be the key part of the future wireless network with dense small cell traffic and high capacity demand. In this paper, we focus on the design of a high spectral efficiency line-of-sight (LoS) multiple-input multiple-
output (MIMO) system for millimeter wave (mmWave) backhaul using dual-polarized frequency division duplex (FDD). High spectral efficiency is very challenging to achieve for the system due to various physical impairments such as phase noise (PHN), timing offset (TO) as well as the poor condition number of the LoS MIMO. In this paper, we propose a holistic solution containing TO compensation, PHN estimation, precoder/decorrelator optimization of the LoS MIMO for wireless backhaul, and the interleaving of each part. We show that the proposed solution has robust performance with end-to-end spectral efficiency of 60 bits/s/Hz for 8x8 MIMO.
Massive MIMO has been regarded as a key enabling technique for 5G and beyond networks. Nevertheless, its performance is limited by the large overhead needed to obtain the high-dimensional channel information. To reduce the huge training overhead asso
ciated with conventional pilot-aided designs, we propose a novel blind data detection method by leveraging the channel sparsity and data concentration properties. Specifically, we propose a novel $ell_3$-norm-based formulation to recover the data without channel estimation. We prove that the global optimal solution to the proposed formulation can be made arbitrarily close to the transmitted data up to a phase-permutation ambiguity. We then propose an efficient parameter-free algorithm to solve the $ell_3$-norm problem and resolve the phase permutation ambiguity. We also derive the convergence rate in terms of key system parameters such as the number of transmitters and receivers, the channel noise power, and the channel sparsity level. Numerical experiments will show that the proposed scheme has superior performance with low computational complexity.
Cyclic redundancy check (CRC) codes combined with convolutional codes yield a powerful concatenated code that can be efficiently decoded using list decoding. To help design such systems, this paper presents an efficient algorithm for identifying the
distance-spectrum-optimal (DSO) CRC polynomial for a given tail-biting convolutional code (TBCC) when the target undetected error rate (UER) is small. Lou et al. found that the DSO CRC design for a given zero-terminated convolutional code under low UER is equivalent to maximizing the undetected minimum distance (the minimum distance of the concatenated code). This paper applies the same principle to design the DSO CRC for a given TBCC under low target UER. Our algorithm is based on partitioning the tail-biting trellis into several disjoint sets of tail-biting paths that are closed under cyclic shifts. This paper shows that the tail-biting path in each set can be constructed by concatenating the irreducible error events (IEEs) and circularly shifting the resultant path. This motivates an efficient collection algorithm that aims at gathering IEEs, and a search algorithm that reconstructs the full list of error events with bounded distance of interest, which can be used to find the DSO CRC. Simulation results show that DSO CRCs can significantly outperform suboptimal CRCs in the low UER regime.
Forensic science suffers from a lack of studies with high-quality design, such as randomized controlled trials (RCT). Evidence in forensic science may be of insufficient quality, which is a major concern. Results from RCT are criticized for providing
artificial results that are not useful in real life and unfit for individualized prescription. Various sources of collected data (e.g. data collected in routine practice) could be exploited for distinct goals. Obstacles remain before such data can be practically accessed and used, including technical issues. We present an easy-to-use software dedicated to innovative data analyses for practitioners and researchers. We provide 2 examples in forensics. Spe3dLab has been developed by 3 French teams: a bioinformatics laboratory (LaTIM), a private partner (Tekliko) and a department of forensic medicine (Jean Verdier Hospital). It was designed to be open source, relying on documented and maintained libraries, query-oriented and capable of handling the entire data process from capture to export of best predictive models for their integration in information systems. Spe3dLab was used for 2 specific forensics applications: i) the search for multiple causal factors and ii) the best predictive model of the functional impairment (total incapacity to work, TIW) of assault survivors. 2,892 patients were included over a 6-month period. Time to evaluation was the only direct cause identified for TIW, and victim category was an indirect cause. The specificity and sensitivity of the predictive model were 99.9% and 90%, respectively. Spe3dLab is a quick and efficient tool for accessing observational, routinely collected data and performing innovative analyses. Analyses can be exported for validation and routine use by practitioners, e.g., for computer-aided evaluation of complex problems. It can provide a fully integrated solution for individualized medicine.
We propose and demonstrate experimentally the concept of the annular interdigital transducer that focuses acoustic waves on the surface of a piezoelectric material to a single, diffraction-limited, spot. The shape of the transducing fingers follows t
he wave surface. Experiments conducted on lithium niobate substrates evidence that the generated surface waves converge to the center of the transducer, producing a spot that shows a large concentration of acoustic energy. This concept is of practical significance to design new intense microacoustic sources, for instance for enhanced acouto-optical interactions.
