Abstract
Compressive sensing (CS) is an emerging technique for data compression in recent years. In this thesis, it is used to compress electroencephalogram (EEG) signals. CS includes two major principles. The one is the sparsity, and the other is incoherence. However, the EEG signal is not sparse enough. Thus, CS can only recover the compressed EEG signals in low compression ratios. Under high compression ratios, the recovery of compressed EEG signals fails after the compression. The compression ratios where EEG can be reconstructed with high quality is not high enough to let the system become energy-efficient, so the compression will be not meaningful. Thus, we want to find a solution to make CS become practical in compressing EEG signals when high compression ratios are adopted. From surveying literatures, the approaches to increase performance in CS can be separated into three classes. First, design a more strong reconstruction algorithm. Second, find a dictionary where the EEG signals can have sparse presentation in such transform domain. Lastly, combine the CS with other compression techniques. Here we take the first and third approaches to achieve the goal. First of all, we proposed a modified iterative pseudo-inverse multiplication (MIPIM) with the complexity O(KMN) where M is the dimension of the measurements, N is the dimension of the signal, and K is the sparse level. This complexity is lower than the most existing algorithms. Next, we extend MIPIM into a multiple measurements (MMV) algorithm. It is called as simultaneously MIPIM (SMIPIM). This aims at recovering all channel signals at the same time and taking the correlation among channels to increase performance. The SMIPIM can reduce normalized mean square error (NMSE) by 0.06 comparing with the classical algorithms in CS. For the part of combining the CS with other compression techniques, we adopt an existing framework which takes an information from server or receiver node to combine CS and Huffman coding efficiently. The framework was proposed to increase the compression to apply to the telemedicine with EEG signals, but we found a shortcoming. It takes a long computational time on running the algorithm which produces information. It will make the instant telemedicine unavailable because sensors can not transmit data until the information are received. Therefore, we propose an algorithm to replace the existing one. The complexity changes from O(L^5) to O(L^2) where L is the number of channels. In our experiment, our algorithm is faster 10^5 times than the existing one. Finally, we carried out the simulation of entire system. We simulated the framework with our proposed algorithm for computing the information of correlation of channels and our SMIPIM for reconstruction. In a compression ratio 3 : 1, the NMSE is 0.0672, and the original CS framework with Block Sparse Bayesian Learning Bound Optimization (BSBLBO) is 0.1554. On the other hand, depending on the minimum acceptable NMSE which is 0.09 for EEG signals, we have a compression ratio 0.31. Moreover, we take the compression ratio to estimate how many channels we can transmit in a fixed transmission bandwidth. The result shows that the number of channels can increase 16 with Bluetooth 2.0 and 35 with ZigBee for wireless transmission after the work.