Efficient Time-Frequency Domain Algorithm for Real Time Signal Compression

For real time remote health monitoring systems, spontaneous transmission of biological signals is essential. To accomplish this time efficient compression schemes play an important role. In this paper, we propose a sparse encoding algorithm consisting of a wavelet transform based iterative thresholding (WTIT). It reduces the minimal ECG voltage values to zero level. Subsequently, it encodes the ECG signal in time-frequency domain, obtaining a high sparsity level. Compressed Row Huffman Coding (CRHC) algorithm converts the sparse matrices into compressed, transmittable matrices. We apply inverse transforms to reconstruct the transmitted signal and test the performance of encoding and reconstruction in terms of compression ratio (CR), percentage root mean square difference (PRD) and time complexity. Keywords: Remote health monitoring systems, Real time, Wavelet Transform, Iterative thresholding, Transmittable matrix I. INTRODUCTION A typical ECG monitoring device generates volumes of digital data creating a necessity for efficient compression before real time transmission of the signal. Most of the prior research [1-3] assumed ECG signal to be noiseless and would possess definite sparsity levels. However, during ECG signal acquisition, the sparsity level may vary due to mass motion. Also, additive Gaussian noise remains in signal which results into powerline interferences and baseline drifts [4]. For data compression, we have used parameter extraction and wavelet based transformation methods. The sparsity of ECG signal, that can be achieved, is examined to realize the compressibility of the signal through our proposed algorithm involving sparsity accomplishment scheme: WTIT followed by lossless encoding scheme CRHC. While most of the related earlier works [2,3,5] either achieved low PRD, or high CR; in this work, we have achieved lower CR and PRD simultaneously. Also, previous work [6] on ECG compression using wavelet transform assumed an arbitrary threshold value, but the threshold may change in ECG signal due to various cardiovascular diseases. In this paper, the algorithm WTIT determines local threshold depending upon the noise variance at a region. In time-frequency domain, the threshold changes from time to time across the ECG transformed matrices and thus, it is effective in case of any cardiovascular disease a patient might be affected with. In this work, our contribution is to develop an end-to-end model, which (i) filters out noise from the raw ECG signal, (ii) encodes the noiseless signal in form of highly sparse matrices, (iii) converts the sparse matrices into transmittable matrices of much reduced size, (iv) reconstructs the signal using inverse transformations. For real time signal transmission, the processing time plays the key role. The tim of our proposed algorithms is in the order of complexities in the order of O(n 2 ). Section II describes our proposed met Figure 1. General transform based compression II. FRAMEWORK FOR THE COMPRESSION OF ECG SIGNAL Fig. 1 shows the framework on which a set of algorithms are applied for the compression of ECG signal in real time. The continuous wavelet transform , √ ∞ ∞ Here, is the scaling factor, mother wavelet . In discrete wavelet transform, the signal where is the sampling frequency, and low pass filters, and respectively as shown in Fig. 2. Figure 2. DWT of x[n] upto three levels of decomposition The output of the high pass filter after down sampling by a factor of coefficients ( ) and the output of the low pass filter after down sampling by a factor of two yields approximate coefficients ( ). International Journal of Recent Trends in Engineering & Research (IJRTER) Volume 03, Issue 09; September 2017 O(n), while most the previous related works had time hod while section III discussed results. Section IV , of any signal at time t can be represented as: ∗ , ∞ ∞ (1) is the translation factor, ∗ is the complex conjugate of the , which is a discrete time signal such that is continuously passed through a set of high pass