Compression of Multidimensional Biomedical Signals with Spatial and Temporal Codebook-Excited Linear Prediction Elias S
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2604 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 11, NOVEMBER 2009 Compression of Multidimensional Biomedical Signals With Spatial and Temporal Codebook-Excited Linear Prediction Elias S. G. Carotti, Member, IEEE, Juan Carlos De Martin, Member, IEEE, Roberto Merletti, Senior Member, IEEE, and Dario Farina*, Senior Member, IEEE Abstract—In this paper, we propose a model-based lossy cod- mounted on the subject, e.g., in ergonomics or sport-related ing technique for biomedical signals in multiple dimensions. The studies. In these applications, signal compression is highly de- method is based on the codebook-excited linear prediction ap- sirable to reduce the bandwidth needed to transmit or store the proach and models signals as filtered noise. The filter models short- term redundancy in time; the shape of the power spectrum of the signals while preserving their relevant information content. signal and the residual noise, quantized using an algebraic code- Extensive work has been performed on biomedical signal book, is used for reconstruction of the waveforms. In addition compression [3], [4]. Although in some cases, lossless tech- to temporal redundancy, redundancy in the coding of the filter niques have been applied [5], the research has focused mostly and residual noise across spatially related signals is also exploited, on lossy coding. Lossy compression is preferred when the dis- yielding better compression performance in terms of SNR for a given bit rate. The proposed coding technique was tested on sets of tortion introduced by the compression scheme does not affect multichannel electromyography (EMG) and EEG signals as rep- the clinical relevance of the reconstructed signal. Several tech- resentative examples. For 2-D EMG recordings of 56 signals, the niques have been previously proposed for lossy compression coding technique resulted in SNR greater than 3.4 ± 1.3 dB with of single-channel biomedical signals (e.g., see [7]–[10]); these respect to independent coding of the signals in the grid when the methods usually perform a transformation of the signal in a compression ratio was 89%. For EEG recordings of 15 signals and the same compression ratio as for EMG, the average gain in SNR domain where the signal energy is distributed across a few co- was 2.4 ± 0.1 dB. In conclusion, a method for exploiting both efficients. For example, Brechet at al. [11] recently proposed the temporal and spatial redundancy, typical of multidimensional a lossy coding technique for single-channel biomedical signals biomedical signals, has been proposed and proved to be superior based on the wavelet packet transform [discrete packet wavelet to previous coding schemes. transform (DPWT)] and modified embedded zero-tree coding Index Terms—EEG, electromyography (EMG), lossy compres- [embedded zero-tree wavelet (EZW)]. sion, multichannel signals. Single-channel coding techniques are based on removing the temporal redundancy in the signal. In multichannel recordings, I. INTRODUCTION in addition to temporal correlations within each channel, signif- ANY diagnostic and monitoring activities require long- icant correlation may also be present across the channels; the M duration recordings of biomedical signals, such as elec- spatial correlation depends on the nature of the signal sources tromyography (EMG), ECG, or EEG. The amount of data to be and on the location of the detecting sensors. Exploiting the in- transferred or stored may be very large. For example, surface terchannel correlation would probably result in more efficient EMG signals are usually acquired at 12–16 bits/sample, with coding of the data with possibly lower distortion. However, rel- sampling rate ranging from 1 to 10 kHz, and in some applica- atively few studies have addressed compression of multichannel tions, are recorded continuously for hours, e.g., for monitoring biomedical recordings [12]. muscles during working activities [1]. In addition, several types Although, in principle, it would be possible to adapt com- of detection systems can be applied on the same patient, leading pression techniques developed for video sequence coding to to multichannel recordings [2], [3]. multidimensional biomedical signals, these methods would be In some cases, the acquisition system is not directly con- suboptimal for the specific application. Biological signals, al- nected to the processing system. This can be either the case though significantly spatially correlated, can, indeed, be consid- of telemedicine or acquisition systems transferring data with ered wide-sense stationary (WSS) for longer time intervals than wireless technology, which allows reducing the size of devices video sequences, for which usually only neighboring frames are interpolated for prediction [13], [14]. For example, in static Manuscript received October 31, 2008; revised April 21, 2009. First published conditions surface, EMG signals are often considered WSS for July 28, 2009; current version published October 16, 2009. Asterisk indicates time intervals of up to 1–2 s [15]; these signals can be efficiently corresponding author. E. S. G. Carotti and J. C. De Martin are with the Dipartimento di Automatica modeled with antireflection (AR) all-pole filters of limited or- e Informatica (DAUIN), Politecnico di Torino, Turin 10129, Italy. der [16], and thus, have characteristics more similar to speech R. Merletti is with the Laboratorio di Ingegneria del Sistema Neuromuscolare or audio signals than to video sequences. (LISiN), Dip. di Elettronica, Politecnico di Torino, Turin 10129, Italy. *D. Farina is with the Center for Sensory-Motor Interaction (SMI), Depart- In this paper, we propose a new multidimensional compres- ment of Health Science and Technology, Aalborg University, Aalborg, DK-9220, sion technique based on AR modeling, and aim at exploiting Denmark (e-mail: [email protected]). both the temporal intrachannel and the spatial interchannel Digital Object Identifier 10.1109/TBME.2009.2027691 0018-9294/$26.00 © 2009 IEEE Authorized licensed use limited to: Politecnico di Torino. Downloaded on January 19, 2010 at 09:43 from IEEE Xplore. Restrictions apply. CAROTTI et al.: COMPRESSION OF MULTIDIMENSIONAL BIOMEDICAL SIGNALS 2605 minimizes the mean-squared error in the reconstruction of the signal. In this study, the signals are divided into 160-sample frames, although different frame lengths are possible. Each 160-sample frame is further divided into 40-sample subframes. AR param- eters are then computed from these subframes. The AR model order depends on the application. For example, an order of 10 was shown to be appropriate for surface EMG spectral de- scription [7]. AR coefficients are estimated from the second and fourth subframes, and linear interpolation is applied for the model parameters of the remaining subframes, i.e., they are es- timated as the means of the corresponding parameters from the preceding and the subsequent subframes, which are available to both the encoder and the decoder. The AR coefficients are com- puted from the signal autocorrelation [17]. Since the variance of Fig. 1. Block diagram of the proposed technique. The AR model parameters the estimate of the autocorrelation function decreases with the are estimated for each channel, then the interchannel dependency is removed number of samples used for its estimate, 80 samples were used between both the LSF parameters and the prediction residual data using past for the estimation of the autocorrelation. coded data from spatially adjacent signals. The resulting residual error signal is vectorially quantized by means of analysis-by-synthesis. See text for details. The floating point AR coefficients are transformed into the line spectral frequencies (LSF) representations to assure quanti- zation and interpolation efficiency, and filter stability [18]. The correlation of the signals. The technique can be applied to any two STP filters from the second and fourth subframes are then multidimensional recording and will be tested on two represen- jointly quantized with split matrix quantization of a first-order tative examples of multichannel biomedical signals (EEG and moving average (MA) prediction residual [19]. Finally, the pre- EMG). diction residual signal of each 40-sample subframe is coarsely quantized into a number of unitary pulses and a gain by means of an algebraic codebook, and analysis-by-synthesis to minimize II. METHODS the mean-squared error of the whole reconstruction signal [21]. We assume to operate on multidimensional signals, with time CELP coding of speech signals would perform an intermediate as one of the dimensions; the other dimensions represent spatial step, called long-term prediction (LTP), before quantization of information. For example, multichannel EEG and EMG signals the residual data, aimed at removing long-term redundancy due have one temporal and two spatial dimensions. These recordings to the voice pitch [20], [22]. This characteristic is not present can be considered as a collection of correlated waveforms char- in the biomedical signals considered, and thus, the LTP was not acterized by both temporal redundancy (within the single wave- included in the proposed method. form) and spatial redundancy (across waveforms). Effective compression techniques should maximally reduce both types B. Spatial Correlation Across Power Spectra of redundancy. Fig. 1 depicts a block diagram of the proposed technique, Multidimensional recordings are usually not spatially white. which is detailed in the following. Therefore, it is expected that