Remote activity monitoring can support aging-in-place for the elderly, providing crucial capabilities such as fall detection. Falls are the leading cause of accidental death in people aged 65 and over in the United States. The chances of survival are high with low impact on quality of life when prompt assistance is provided after a fall. Radar is at the forefront of research on non-wearable technologies for fall detection and monitoring of activities of daily living for eldercare. Various features extracted from Doppler motion signatures have been proposed in the literature for radar-based fall detection. However, none of these features were specifically designed to provide the most discrimination between the fall and non-fall motion classes. In this paper, we perform linear discriminant analysis (LDA) of Doppler signatures as a first step towards identification of the most discriminative features. LDA performance is evaluated using real data measurements of various indoor human activities and compared with that of existing radar-based fall detection schemes.
Rank-1 L1-norm-based TUCKER2 (L1-TUCKER2) decomposition of 3-way tensors was recently solved exactly, for the first time, by Markopoulos et al.<sup>1</sup> The exact solution to general-rank L1-TUCKER2 remains to date unknown. In this work, we present a novel approximate algorithm for general-rank L1-TUCKER2 decomposition of 3-way tensors. Our algorithm is accompanied by formal convergence and complexity analysis. Our numerical studies illustrate the sturdy corruption resistance of the proposed algorithm compared to state-of-the-art TUCKER2-decomposition counterparts such as GLRAM, HOSVD, and HOOI.
We present a novel method for robust tracking in video frame sequences via L1-Grassmann manifolds. The proposed method represents adaptively the target as a point on the Grassmann manifold, calculated by means of L1-norm Principal-Component Analysis (L1-PCA). For this purpose, an efficient algorithm for adaptive L1-PCA is presented. Our experimental studies illustrate that the presented tracking method, leveraging the outlier resistance of L1-PCA, demonstrates robustness against target occlusions and illumination variations.
Proc. SPIE. 10211, Compressive Sensing VI: From Diverse Modalities to Big Data Analytics
KEYWORDS: Transmitters, Modulation, Data hiding, Matrices, Receivers, Phase shift keying, Linear filtering, Telecommunications, Information technology, High dynamic range imaging, Picosecond phenomena, Binary data
We introduce maximum-SINR, sparse-binary waveforms that modulate data information symbols over the entire continuum of the available/device-accessible spectrum. We present an optimal algorithm that designs the proposed waveforms by maximizing the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum- SINR linear filter at the receiver. In addition, we propose a suboptimal, computationally-efficient algorithm. Simulation studies compare the proposed sparse-binary waveforms with their conventional non-sparse binary counterparts and demonstrate their superior SINR performance. The post-filtering SINR and bit-error rate (BER) improvements attained by the proposed waveforms are also experimentally verified in a software-defined radio testbed operating in multipath laboratory environment, in the presence of colored interference.
Standard Principal-Component Analysis (PCA) is known to be very sensitive to outliers among the processed data.<sup>1</sup> On the other hand, it has been recently shown that L1-norm-based PCA (L1-PCA) exhibits sturdy resistance against outliers, while it performs similar to standard PCA when applied to nominal or smoothly corrupted data.<sup>2, 3</sup> Exact calculation of the <i>K</i> L1-norm Principal Components (L1-PCs) of a rank-<i>r</i> data matrix <strong>X</strong>∈ R<sup><i>D×N</i></sup> costs <i>O</i>(2<sup><i>NK</i></sup>), in the general case, and <i>O</i>(<i>N<sup>(r-1)K+1</sup></i>) when <i>r</i> is fixed with respect to <i>N</i>.<sup>2, 3</sup> In this work, we examine approximating the <i>K</i> L1-PCs of <strong>X</strong> by the <i>K</i> L1-PCs of its L2-norm-based rank-<i>d</i> approximation (<i>K≤d≤r</i>), calculable exactly with reduced complexity <i>O</i>(<i>N<sup>(d-1)K+1</sup></i>). <i>Reduced-rank L1-PCA</i> aims at leveraging both the low computational cost of standard PCA and the outlier-resistance of L1-PCA. Our novel approximation guarantees and experiments on dimensionality reduction show that, for appropriately chosen <i>d</i>, reduced-rank L1-PCA performs almost identical to L1-PCA.
Conventional subspace-based signal direction-of-arrival estimation methods rely on the familiar L<sub>2</sub>-norm-derived
principal components (singular vectors) of the observed sensor-array data matrix. In this paper, for the first
time in the literature, we find the L<sub>1</sub>-norm maximum projection components of the observed data and search
in their subspace for signal presence. We demonstrate that L<sub>1</sub>-subspace direction-of-arrival estimation exhibits
(i) similar performance to L<sub>2</sub> (usual singular-value/eigen-vector decomposition) direction-of-arrival estimation
under normal nominal-data system operation and (ii) significant resistance to sporadic/occasional directional
jamming and/or faulty measurements.