Spatiotemporal Sparse Bayesian Learning with Applications to Compressed Sensing of Multichannel Physiological Signals

Energy consumption is an important issue in continuous wireless telemonitoring of physiological signals. Compressed sensing (CS) is a promising framework to address it, due to its energy-efficient data compression procedure. However, most CS algorithms have difficulty in data recovery due to non-sparsity characteristic of many physiological signals. Block sparse Bayesian learning (BSBL) is an effective approach to recover such signals with satisfactory recovery quality. However, it is time-consuming in recovering multichannel signals, since its computational load almost linearly increases with the number of channels. This work proposes a spatiotemporal sparse Bayesian learning algorithm to recover multichannel signals simultaneously. It not only exploits temporal correlation within each channel signal, but also exploits inter-channel correlation among different channel signals. Furthermore, its computational load is not significantly affected by the number of channels. The proposed algorithm was applied to brain computer interface (BCI) and EEG-based driver's drowsiness estimation. Results showed that the algorithm had both better recovery performance and much higher speed than BSBL. Particularly, the proposed algorithm ensured that the BCI classification and the drowsiness estimation had little degradation even when data were compressed by 80%, making it very suitable for continuous wireless telemonitoring of multichannel signals.Comment: Codes are available at: https://sites.google.com/site/researchbyzhang/stsb

Compressive Sensing with Low-Power Transfer and Accurate Reconstruction of EEG Signals

Tele-monitoring of EEG in WBAN is essential as EEG is the most powerful physiological parameters to diagnose any neurological disorder. Generally, EEG signal needs to record for longer periods which results in a large volume of data leading to huge storage and communication bandwidth requirements in WBAN. Moreover, WBAN sensor nodes are battery operated which consumes lots of energy. The aim of this research is, therefore, low power transmission of EEG signal over WBAN and its accurate reconstruction at the receiver to enable continuous online-monitoring of EEG and real time feedback to the patients from the medical experts. To reduce data rate and consequently reduce power consumption, compressive sensing (CS) may be employed prior to transmission. Nonetheless, for EEG signals, the accuracy of reconstruction of the signal with CS depends on a suitable dictionary in which the signal is sparse. As the EEG signal is not sparse in either time or frequency domain, identifying an appropriate dictionary is paramount. There are a plethora of choices for the dictionary to be used. Wavelet bases are of interest due to the availability of associated systems and methods. However, the attributes of wavelet bases that can lead to good quality of reconstruction are not well understood. For the first time in this study, it is demonstrated that in selecting wavelet dictionaries, the incoherence with the sensing matrix and the number of vanishing moments of the dictionary should be considered at the same time. In this research, a framework is proposed for the selection of an appropriate wavelet dictionary for EEG signal which is used in tandem with sparse binary matrix (SBM) as the sensing matrix and ST-SBL method as the reconstruction algorithm. Beylkin (highly incoherent with SBM and relatively high number of vanishing moments) is identified as the best dictionary to be used amongst the dictionaries are evaluated in this thesis. The power requirements for the proposed framework are also quantified using a power model. The outcomes will assist to realize the computational complexity and online implementation requirements of CS for transmitting EEG in WBAN. The proposed approach facilitates the energy savings budget well into the microwatts range, ensuring a significant savings of battery life and overall system’s power. The study is intended to create a strong base for the use of EEG in the high-accuracy and low-power based biomedical applications in WBAN

Compressed sensing for enhanced through-the-wall radar imaging

Through-the-wall radar imaging (TWRI) is an emerging technology that aims to capture scenes behind walls and other visually opaque materials. The abilities to sense through walls are highly desirable for both military and civil applications, such as search and rescue missions, surveillance, and reconnaissance. TWRI systems, however, face with several challenges including prolonged data acquisition, large objects, strong wall clutter, and shadowing effects, which limit the radar imaging performances and hinder target detection and localization

Stable super-resolution limit and smallest singular value of restricted Fourier matrices

Super-resolution refers to the process of recovering the locations and amplitudes of a collection of point sources, represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. The recovery process is highly sensitive to noise whenever the distance $\Delta$ between the two closest point sources is less than $1/M$. This paper studies the {\it fundamental difficulty of super-resolution} and the {\it performance guarantees of a subspace method called MUSIC} in the regime that $\Delta<1/M$. The most important quantity in our theory is the minimum singular value of the Vandermonde matrix whose nodes are specified by the source locations. Under the assumption that the nodes are closely spaced within several well-separated clumps, we derive a sharp and non-asymptotic lower bound for this quantity. Our estimate is given as a weighted $\ell^2$ sum, where each term only depends on the configuration of each individual clump. This implies that, as the noise increases, the super-resolution capability of MUSIC degrades according to a power law where the exponent depends on the cardinality of the largest clump. Numerical experiments validate our theoretical bounds for the minimum singular value and the resolution limit of MUSIC. When there are $S$ point sources located on a grid with spacing $1/N$, the fundamental difficulty of super-resolution can be quantitatively characterized by a min-max error, which is the reconstruction error incurred by the best possible algorithm in the worst-case scenario. We show that the min-max error is closely related to the minimum singular value of Vandermonde matrices, and we provide a non-asymptotic and sharp estimate for the min-max error, where the dominant term is $(N/M)^{2S-1}$.Comment: 47 pages, 8 figure