Pruning-Based Sparse Recovery for Electrocardiogram Reconstruction from Compressed Measurements

Figures

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  Figure 1. Illustration of conventional orthogonal matching pursuit (OMP) and recovery based on tree search where the true paths contain only elements in the support T, and incorrect paths consist of at least one element from Tc. While OMP does not provide any further chances after it selects an incorrect index in the second layer (a), multiple path investigation in (b) enables a reduction in the misdetection of the support element.

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  Figure 2. Basic structure of ECG compression and reconstruction. Note that the reconstruction is based on the discrete cosine transform (DCT) basis (s^), while compression is performed in the time domain (y=Φx).

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  Figure 3. Illustration of the proposed method when |Θ|=4 and K=3. The branches of each node consist of only the elements in Θ, and the paths with large cost functions are removed from the search.

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  Figure 4. Examples of the tested ECG samples in our simulations and the reconstructed signal for each sample signal by tree pruning-based matching pursuit (TPMP) at compression ratio (CR) =65, where the solid and dotted lines denote the original ECG (x) and the reconstructed ECG (x^=Ψs^), respectively.

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  Figure 5. ECG reconstruction using the proposed method when N=1000 and K=100 where the solid and dotted lines denote the original ECG (x) and the reconstructed ECG (x^=Ψs^), respectively.

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  Figure 6. Exact recovery ratio (ERR) performance of the sparse signal recovery methods when N=1000 and K=100.

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  Figure 7. Percentage root-mean-square difference (PRD) performance of the sparse signal recovery methods when N=1000 and K=100.

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  Figure 8. Complexity of the sparse signal recovery methods when N=1000 and K=100.

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  Figure 9. PRD performance of the sparse signal reconstruction from noisy measurements.

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  Figure 10. Average running time complexity of the sparse signal reconstruction from noisy measurements.