Signal, Image and Video Processing https://doi.org/10.1007/s11760-019-01441-4 ORIGINAL PAPER A novel recursive backtracking genetic programming-based algorithm for 12-lead ECG compression Mohammad Feli 1 · Fardin Abdali-Mohammadi 1 Received: 13 March 2018 / Revised: 11 January 2019 / Accepted: 2 February 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019 Abstract ECG signal is among medical signals used to diagnose heart problems. A large volume of medical signal’s data in telemedicine systems causes problems in storing and sending tasks. In the present paper, a recursive algorithm with backtracking approach is used for ECG signal compression. This recursive algorithm constructs a mathematical estimator function for each segment of the signal using genetic programming algorithm. When all estimator functions of different segments of the signal are determined and put together, a piecewise-defined function is constructed. This function is utilized to generate a reconstructed signal in the receiver. The compression result is a set of compressed strings representing the piecewise-defined function which is coded through a text compression method. In order to improve the compression results in this method, the input signal is smoothed. MIT-BIH arrhythmia database is employed to test and evaluate the proposed algorithm. The results of this algorithm include the average of compression ratio that equals 30.97 and the percent root-mean-square difference that is equal to 2.38%, suggesting its better efficiency in comparison with other state-of-the-art methods. Keywords Electrocardiograph · Signal compression · Genetic programming · Backtracking algorithm 1 Introduction Telemedicine technologies that have been developed in recent years have allowed storing and sending medical sig- nals for different applications. Analysis of ECG signal is the most common method of diagnosing heart disease, i.e., the most frequent disease of the current century. Extraction and identification of ECG signal in electrocardiography monitor- ing systems lead to the production of a large volume of data. However, the memory limitations in storing and bandwidth in the network are considered as an important challenge in such systems. Therefore, the reduction in information content for storing and sending ECG signal has turned ECG compression into a considerable challenge. In general, compression algorithms are classified into two groups of lossless and lossy algorithms [1,2]. In lossless methods, the reconstructed signal is exactly the same as the original signal. Nevertheless, such methods do not have extraordinary compression results. Hence, these methods B Fardin Abdali-Mohammadi fardin.abdali@razi.ac.ir 1 Department of Computer Engineering and Information Technology, Razi University, Kermanshah, Iran are often used as a compound method with other tech- niques. Run-length, Huffman, arithmetic, and Lempel–Ziv (LZ) family coding are among these methods [3]. Although the original signal reconstruction is accompanied by some errors in lossy methods, this type of compression method produces acceptable results. Lossy methods consist of three groups of different tech- niques. The first group is direct compression techniques often considered as traditional methods of ECG compres- sion. AZTEC, TP, CORTES, FAN, and SAPA are examples of direct methods [3,4]. Transform-based techniques make up the second group of lossy compression methods. In such methods, ECG data are transformed from the initial space to another one, and compression is done on data in the new domain. Discrete cosine transform (DCT) [5], Karhunen–Loeve transform (KLT) [6,7], and wavelet trans- form methods [8–12] could be considered as such techniques. The third group of lossy methods is parameter extraction techniques. These methods usually work based on model- ing and do modeling by extracting different features from the input raw signal. Mathematical modeling [13,14], linear prediction-based methods [15,16], modeling based on vector quantization [17,18], and modeling based on pattern match- ing [19] are among such techniques. 123