3.1. History

This section provides a historical review of some of the popular compression techniques for ECG data compression. This review is by no means complete. The focus is on compressive sensing-based techniques where the encoders are simple and most of the complexity lies in the decoding.

In wireless body area networks (WBAN) based telemonitoring networks[9], the energy consumption on sensor nodes is a primary design constraint [24]. The wearable sensor nodes are often battery-operated. It is necessary to reduce energy consumption as much as possible.

However, long-term ECG monitoring can generate a large amount of uncompressed data. For example, each half-hour 2 lead recording in the MIT-BIH Arrhythmia database [25] requires 1.9MB of storage. As shown in [22], in a real-time telemonitoring sensor node, the wireless transmission of data consumes most of the energy. The real-time compression of ECG data by a low-complexity encoder has received significant attention in the past decade.

ECG signal compression has been an active area of interest for several decades. Extensive surveys can be found in [30, 31]. Compressive sensing (CS) based techniques for ECG data compression have been reviewed in [11, 19].

3.1.1. Transform Domain Techniques

Transform domain techniques (e.g., Discrete Cosine Transform [1], Discrete Cosine Transform [4, 5], Discrete Wavelet Transform [12, 17, 20, 29]) are popular in ECG compression and achieve high compression ratios (CR) at clinically acceptable quality. However, they require computationally intensive sparsifying transforms on all data samples and are thus not suitable for WBAN sensor nodes [11].

3.1.2. Compressive Sensing Approaches

Compressive sensing [3, 6, 7, 8, 13] uses a sub-Nyquist sampling method by acquiring a small number of incoherent measurements which are sufficient to reconstruct the signal if the signal is sufficiently sparse in some basis. For a sparse signal \(\bx \in \RR^n\), one would make \(m\) linear measurements where \(m \ll n\) which can be mathematically represented by a sensing operation

\[ \by = \Phi \bx \]

where \(\Phi \in \RR^{m \times n}\) is a matrix representation of the sensing process and \(\by \in \RR^m\) the set of \(m\) measurements collected for \(\bx\). A suitable reconstruction algorithm can recover \(\bx\) from \(\by\).

Ideally, the sensing process should be implemented at the hardware level in the analog-to-digital conversion (ADC) process. However, much of the use of CS in ECG follows a digital CS paradigm [22] where the ECG samples are acquired first by the ADC circuit on the device and then they are translated into incoherent measurements via the multiplication of a digital sensing matrix. These measurements are then transmitted to remote telemonitoring servers. A suitable reconstruction algorithm is used on the server to recover the original ECG signal from the compressive measurements. Reconstruction algorithms for ECG signals include: greedy algorithms [27] (simultaneous orthogonal matching pursuit), optimization-based algorithms [33], [22] (SPG-L1), Bayesian learning based algorithms [34, 35, 36], deep learning based algorithms [32].

To keep the sensing matrix multiplication simple and efficient, sparse binary sensing matrices are a popular choice [22, 35].

3.1.2.1. Entropy Coding

The literature on the use of CS for ECG compression is mostly focused on the design of the specific sensing matrix, sparsifying dictionary, or reconstruction algorithm for the high-quality reconstruction of the ECG signal from the compressive measurements. To the best of our knowledge, (digital) quantization and entropy coding of the compressive measurements of ECG data hasn’t received much attention in the past.

Mamaghanian et al.[22] use a Huffman codebook which is deployed inside the sensor device. They don’t use any quantization of the measurements. However, they don’t provide much detail on how the codebook was designed or how should it be adapted for variations in ECG signals. They clearly define the compression ratio in terms of a ratio between the uncompressed bits \(\bits_u\) and the compressed bits \(\bits_c\). They define it as \(\frac{\bits_u - \bits_c}{\bits_u} \times 100\). This is often known in the literature as percentage space savings.

Simulation-based studies often send the real-valued compressive measurements to the decoder modules and don’t consider the issue of the number of bits required to encode each measurement. Zhang et al. [35] and Zhang et al. [32] define \(\frac{n - m}{n} \times 100\) as compression ratio. Mangia et al. [23] define \(\frac{n}{m}\) as the compression ratio. Polania et al. [28] define \(\frac{m}{n}\) as compression ratio. Picariello et al. [26] use a non-random sensing matrix. They infer a circulant binary sensing matrix directly from the ECG signal being compressed. The sensing matrix is adapted as and when there is a significant change in the signal statistics. They represent both the ECG samples and compressive measurements with the same number of bits per sample/measurement. However, in their case, there is the additional overhead of sending the sensing matrix updates. Their compression ratio is slightly lower than \(\frac{n}{m}\) where they call \(\frac{n}{m}\) as the under-sampling ratio.

Huffman codes have frequently been used in ECG data compression for non-CS methods. Luo et al. in [21] proposed a dynamic compression scheme for ECG signals which consisted of a digital integrate and fire sampler followed by an entropy coder. They used Huffman codes for entropy coding of the timestamps associated with the impulse train. Chouakri et al. in [10] compute the DWT of ECG signal by Db6 wavelet, select coefficients using higher order statistics thresholding, then perform linear prediction coding and Huffman coding of the selected coefficients.

Asymmetric Numeral Systems (ANS) ([14]) based entropy coding schemes have seen much success in recent years for lossless data compression. The zstd library by Facebook Inc. [39] and LZFSE by Apple Inc. are popular lossless data compression formats based on ANS. To the best of our knowledge, ANS-type stream codes have not been considered in the past for the entropy coding of compressive measurements.