Sparse Signal Acquisition via Compressed Sensing and Principal Component Analysis

Abstract

This paper presents a way of acquiring a sparse signal by taking only a limited number of samples; sampling and compression are performed in one step by the analog to information conversion. The signal is recovered with minimal information loss from the reduced data record via compressed sensing reconstruction. Several methods of analog to information conversion are described with focus on numerical complexity and implementation in existing embedded devices. Two novel analog to information conversion methods are proposed, distinctive by their computational simplicity - direct subsampling and subsampling with integration. Proposed sensing methods are intended for and evaluated with real water parameter signals measured by a wireless sensor network. Compressed sensing proves to reduce the data transfer rate by >80 % with very little signal processing performed at the sensing side and no appreciable distortion of the reconstructed signal.

Compressed sensing with continuous parametric reconstruction

“…Both K and could also be found by an educated guess or by trial and error, since they are small numbers by the nature of model (14). The study [22] utilized CS with DLR based on extensive trained dictionary. Methods such as orthogonal matching pursuit, iterative hard thresholding, CoSaMP etc.…”

“…The authors investigated CS application in this network because of tight energy budget, which can potentially be improved by lowering the sampling frequency. Results of previous investigation [22] of conventional DLR CS in the same network will be provided as reference.…”

“…Data acquired by the WSN described above show that signals of all the measured parameters correlate and display the same basic pattern. A typical signal contains a large slowly changing DC component, a faster AC component with relatively small amplitude and a small amount of noise [22]. Examples are shown in Figure 6.…”

“…Reconstruction is conventionally based on a basis matrix defining signal features, [21] or using methods such as principal component analysis [22][23][24][25], feature extraction [26][27][28] or methods of machine learning [29][30][31]. A number of reconstruction methods have been established, (orthogonal) matching pursuit [32], CoSaMP [33], iterative hard thresholding [33] or matrix pseudoinverse [22] are commonly used. None of these methods is truly versatile, some are more advantageous in a certain application than others.…”

Optimization Paradigm in the Signal Recovery after Compressive Sensing

“…Requirement on the incoherency between matrices Φ and Ψ is achieved by taking subsequently successive M chipping blocks pm(i) with the length I from the whole PRBS with the length MI. According to equation 4 [15], [16]. Compressed digital data stream y of M samples is transmitted to the receiving block.…”