Time-Frequency Domain Compression mainly focuses wavelet based compression algorithms.
This method is given higher important because of its good localization properties in time and fre- quency domains, high energy compaction capability and easy implementation. Wavelet based meth- ods outperform the traditional time domain and frequency domain ECG compression methods [72].
In time-frequency plane the main algorithmic steps are 1) Amplitude normalization, 2) Period normal- ization, 3) Wavelet transform, and 4) Encoding of wavelet coefficients.
The resulting wavelet coefficients are encoded to achieve the compression. In existing literature, encoding of the wavelet coefficients are found based on 1) Threshold Methods [72–85], 2) Embedded Coding Methods [86–90], 3) Vector Quantization (VQ) Methods [91–95].
For signal decomposition there are methods such as, Short Time Fourier Transform (STFT), WignerVille Transform (WVT), ChoiWilliams Distribution (CWD) and the Wavelet Transform (WT).
The STFT uses a single analysis window of fixed length in both time and frequency domains. This is a major drawback of the STFT. For proper analysis, it requires a shorter window in time domain for the high frequency content of a signal and a longer window length for the low frequency content of the signal. This is like contractions and dilations of the basis wavelet. The Discrete Wavelet Transform (DWT) is become the most desirable tool for ECG analysis. It makes easy to interpret resulting trans- formed signal in time-frequency domain. This linear process performs decomposition of ECG signal separating it into components, that appear at different scales. The dilation of the mother wavelet gives the low frequency components whereas translation represents the high frequency components.
The efficiency of wavelet analysis is its fast pyramid algorithm. The algorithm has the forward
1.6 Wavelet Transform and ECG Signal
algorithm (decomposition structure) to compute the DWT and backward algorithm (reconstruction structure) to compute the Inverse Discrete Wavelet Transform (IDWT). The forward algorithm uses low-pass and high-pass linear filters to decompose the signal into low-frequency and high-frequency subbands. It has down-sampling operations which speed-up the algorithm. The reconstruction or inverse process performs the up-sampling operation with linear filtering.
The ECG signal under evaluation passes through two complementary filters which give low-pass and high-pass components. The decomposition process may be iterative with successive low fre- quency components. In the process, the signal is broken down into many lower-resolution compo- nents. To reach the desired decomposition level, the iteration is repeated.
The Hybrid Compression Methods (HCM’s) for ECG signal are some combination of the coding algorithms [93, 94, 96–99]. Compression methods under this category result in good compression performance with the cost of increased time and space complexity. These methods are suitable for off-line processing for the acceptable distortion level provided by the clinician.
The wavelet transform is found suitable for compression of ECG signal which gives a good recon- struction [100]. Thakor et al. [101] presented a multiwave ECG compression method by preserving the coarse sub-signals and discarding the differential sub-signals decomposed by the orthonormal wavelet transform. Best reconstruction results are obtained with vector quantization (VQ) on scales with long duration and low dynamic range, and scalar quantization on scales of short duration and high dynamic range [91]. Nagarajan et al. [72] presented a constraint ECG compression by introduc- ing a constraint on PRD and using adaptive wavelet packet decomposition. ECG coding by wavelet based linear prediction based on beat segmentation, and period normalization (PN) is proposed by Ramakrishnan and Saha [97]. A series of experiments are performed to evaluate the ability of the Embedded Zerotree Wavelet (EZW) algorithm to compress ECG data and to identify which wavelet performs the best using the ECG data taken from themitctdatabase [86]. However, the EZW algo- rithm yields worse performance than the DWT because the best basis decomposition often splits the signal into a number of smaller hierarchies that cannot be efficiently encoded [84].
Chen and Itoh [73] presented a new ECG compression method based on orthonormal wavelet transform along with an adaptive quantization strategy. It is shown a predetermined PRD can be guaranteed with high compression ratio and low implementation complexity. For a mobile telecar-
diogram system, an Optimal Zonal Wavelet Based Compression (OZWC) method successfully transmit the compressed ECG at a standard GSM data rate of 9.6 kbps [75].
The Set Partitioning in Hierarchical Trees (SPIHT) scheme has received widespread recog- nition for its notable success in image and audio coding. A wavelet ECG codec based on the set partitioning SPIHT) compression algorithm is proposed by Lu et al. [87]. Rajoub [77] proposed a wavelet based ECG data compression algorithm using the BiorSpline (bior4.4) wavelet. It shows better performance than SPIHT coder in terms of PRD. Benzid et al. [79] have reported an ECG compression method based on the pyramidal wavelet decomposition. The resultant coefficients are subjected to an iterative thresholding till a fixed percentage of wavelet coefficients are zeroed out. Ku et al. [81] have proposed an ECG compression method based on the one-dimensional Nonrecursive Discrete Periodized Wavelet Transform (NRDPWT). Kim et al. [80] presented a wavelet transform based ECG compression method with a low delay property for continuous ECG transmission suitable for telecardiology applications over a wireless network. It employs waveform partitioning, adaptive frame size adjustment, wavelet compression, flexible bit allocation and header compression to at- tain low delay and high quality. Blanco et al. [84] presented a Wavelet Packets (WP’s) thresholding based ECG compression method. The number of WP layers is set to 4 and the Cohen-Daubechies- Feauveau 9/7 (bior9.7) is used for decomposition. The performance is compared with SPIHT coding scheme. Manikandan and Dandapat [83] have reported wavelet threshold based ECG signal com- pression technique using Uniform Scalar Zero Zone Quantizer (USZZQ) and Huffman coding on Differencing Significance Map (DSM). WT coefficients in each subband are thresholded based on the Energy Packing Efficiency (EPF) and quantized with uniform scalar zero zone quantizer. Indices of the significant coefficients (significance map) are encoded by applying Huffman coding on the dif- ferences between indices in the significance map. Another two novel wavelet threshold based ECG compression algorithms are proposed for real-time applications [102] which take account of Target Distortion Level (TDL) and Target Data Rate (TDR). In recent, Cheng et al. [103], have proposed wavelet-Based ECG data compression system with linear quality control scheme. Kim et. al. [104]
have reported an ECG signal processing with Quad Level Vector (QLV) for holster system. The compression is achieved by using ECG skeleton and the Huffman coding.