The paper presents a number of results regarding the construction of specific overcomplete dictionaries for ECG compressed sensing (CS). The dictionaries were built using normal and patological cardiac patterns extracted from 24 recordings of the MIT-BIH Arrhythmia Database. It has been shown that the compression results obtained using the CS concept based on specific dictionaries are better that those using the wavelet overcomplete dictionaries. Starting from the concept of sparse signal with respect to a given overcomplete dictionary the paper present several results regarding the possibility of simple pattern classification as well

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper a novel formulation of the optimization problem is proposed, in the form of a rank-constrained nearest correlation matrix problem. Furthermore, improvements for three existing optimization algorithms are introduced, which are shown to be particular instances of the proposed formulation. Simulation results show notable improvements and superior robustness in sparse signal recovery.

Analysis based reconstruction has recently been introduced as an alternative to the well-known synthesis sparsity model used in a variety of signal processing areas. In this paper we convert the analysis exact-sparse reconstruction problem to an equivalent synthesis recovery problem with a set of additional constraints. We are therefore able to use existing synthesis-based algorithms for analysis-based exact-sparse recovery. We call this the Analysis-By-Synthesis (ABS) approach. We evaluate our proposed approach by comparing it against the recent Greedy Analysis Pursuit (GAP) analysisbased recovery algorithm. The results show that our approach is a viable option for analysis-based reconstruction, while at the same time allowing many algorithms that have been developed for synthesis reconstruction to be directly applied for analysis reconstruction as well.

This paper presents a robust reconstruction technique of electrocardiograph (ECG) signals in a compressed sensing based acquisition system, using custom complete and overcomplete dictionaries composed of real ECG patterns. Both signals and atoms are preprocessed segments of ECG recordings. We tested three types of projection matrices and found that the best reconstruction results are obtained when the projection matrix is the product of a random matrix with the transpose of the dictionary used for the sparse representation. Further improvements are obtained by reconstructing every signal multiple times from the same measurements, using different randomized dictionaries, and then averaging all the reconstructions.

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