###### Abstract  
Nowadays, healthcare is becoming very modern, and the support of Internet of Things (IoT) is inevitable in a personal healthcare system. A typical personal healthcare system acquires vital parameters from human users and stores them in a cloud platform for further analysis. Acquiring fundamental biomedical signal, such as with the Electrocardiograph (ECG), is also considered for specific disease analysis in personal healthcare systems. When such systems are scaled up, there is a heavy demand for internet channel capacity to accommodate real time seamless flow of discrete samples of biomedical signals. So, there is a keen need for real time data compression of biomedical signals. Compressive Sensing (CS) has recently attracted more interest due to its compactness and its feature of the faithful reconstruction of signals from fewer linear measurements, which facilitates less than Shannon's sampling rate by exploiting the signal sparsity. The most common biomedical signal that is to be analyzed is the ECG signal, as the prediction of heart failure at an early stage can save a human life. This review is for a vast use-case of IoT framework in which CS measurements of ECG are acquired, communicated through Internet to a server, and the arrhythmia are analyzed using Machine learning (ML). Assuming this use-case specific for ECG, in this review many technical aspects are considered regarding various research components. The key aspect is on the investigation of the best sensing method, and to address this, various sensing matrices are reviewed, analyzed and recommended. The next aspect is the selection of the optimal sparsifying method, and the review recommends unexplored ECG compression algorithms as sparsifying methods. The other aspects are optimum reconstruction algorithms, best hardware implementations, suitable ML methods and effective modality of IoT. In this review all these components are considered, and a detailed review is presented which enables us to orchestrate the use-case specified above. This review focuses on the current trends in CS algorithms for ECG signal compression and its hardware implementation. The key to successful reconstruction of the CS method is the right selection of sensing and sparsifying matrix, and there are many unexplored sparsifying methods for the ECG signal. In this review, we shed some light on new possible sparsifying techniques. A detailed comparison table of various CS algorithms, sensing matrix, sparsifying techniques with different ECG dataset is tabulated to quantify the capability of CS in terms of appropriate performance metrics. As per the use-case specified above, the CS reconstructed ECG signals are to be subjected to ML analysis, and in this review the compressive domain inference approach is discussed. The various datasets, methodologies and ML models for ECG applications are studied and their model accuracies are tabulated. Mostly, the previous research on CS had studied the performance of CS using numerical simulation, whereas there are some good attempts for hardware implementations for ECG applications, and we studied the uniqueness of each method and supported the study with a comparison table. As a consolidation, we recommend new possibilities of the research components in terms of new transforms, new sparsifying methods, suggestions for ML approaches and hardware implementation.  
compressed sensing (CS); electrocardiogram (ECG); biomedical signal; reconstruction; compression ratio; reconstruction accuracy +
Footnote †: journal: Applied Sciences