Multi-base compressive sensing procedure with application to ECG signal reconstruction

Abstract

Standard compressive sensing (CS) scenario assumes a single sparsifying basis used to reconstruct the signals from a small set of incoherent measurements. However, in many cases, the signal cannot be sparsely represented using a single transformation. Particularly, in ECG signal analysis, each signal segment is specific in nature and reflects different physical phenomena. Hence, using the same transformation for all segments may be inappropriate for efficient analysis and reconstruction. Moreover, in the CS scenario, it would be necessary to combine different transforms to achieve compact signal support and to provide successful reconstruction from randomly under-sampled data. This work proposes a hybrid CS reconstruction algorithm that combines different transform basis, based on the concept of orthogonal matching pursuit. The performance of the proposed approach is verified experimentally using the combination of the Fourier and the Hermite transform on the real ECG signals.