This paper deals with designing sensing matrix for compressive sensing systems. Traditionally, the optimal sensing matrix is designed so that the Gram of the equivalent dictionary is as close as possible to a target Gram with small mutual coherence. A novel design strategy is proposed, in which, unlike the traditional approaches, the measure considers of mutual coherence behavior of the equivalent dictionary as well as sparse representation errors of the signals. The optimal sensing matrix is defined as the one that minimizes this measure and hence is expected to be more robust against sparse representation errors. A closed-form solution is derived for the optimal sensing matrix with a given target Gram. An alternating minimization-based algorithm is also proposed for addressing the same problem with the target Gram searched within a set of relaxed equiangular tight frame Grams. The experiments are carried out and the results show that the sensing matrix obtained using the proposed approach outperforms those existing ones using a fixed dictionary in terms of signal reconstruction accuracy for synthetic data and peak signal-to-noise ratio for real images.
Alzheimer's Disease (AD) accounts for 60-70% of all dementia cases, and clinical diagnosis at its early stage is extremely difficult. As several new drugs aiming to modify disease progression or alleviate symptoms are being developed, to assess their efficacy, novel robust biomarkers of brain function are urgently required. This study aims to explore a routine to gain such biomarkers using the quantitative analysis of Electroencephalography (QEEG). This paper proposes a supervised classification framework which uses EEG signals to classify healthy controls (HC) and AD participants. The framework consists of data augmentation, feature extraction, K-Nearest Neighbour (KNN) classification, quantitative evaluation and topographic visualisation. Considering the human brain either as a stationary or a dynamical system, both frequency-based and time-frequency-based features were tested in 40 participants. Results: a) The proposed method can achieve up to 99% classification accuracy on short (4s) eyes open EEG epochs, with the KNN algorithm that has best performance when compared to alternative machine learning approaches; b) The features extracted using the wavelet transform produced better classification performance in comparison to the features based on FFT; c) In the spatial domain, the temporal and parietal areas offer the best distinction between healthy controls and AD. The proposed framework can effectively classify HC and AD participants with high accuracy, meanwhile offering identification and localisation of significant QEEG features. These important findings and the proposed classification framework could be used for the development of a biomarker for the diagnosis and monitoring of disease progression in AD.
In this paper, an adaptive fixed‐time fault‐tolerant control scheme is presented for rigid spacecraft with inertia uncertainties and external disturbances. By using an inverse trigonometric function, a novel double power reaching law is constructed to speed up the state stabilization and reduce the chattering phenomenon simultaneously. Then, an adaptive fixed‐time fault‐tolerant controller is developed for the spacecraft with the actuator faults, such that the fixed‐time convergence of the attitude and angular velocity could be guaranteed, and no prior knowledge on the upper bound of the lumped uncertainties is required anymore in the controller design. Comparative simulations are provided to illustrate the effectiveness and superior performance of the proposed scheme.
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