Non-negative constrained dictionary learning for compressed sensing of ECG signals

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Objective. Overcomplete dictionaries are widely used in compressed sensing (CS) to improve the quality of signal reconstruction. However, dictionary learning under the -norm or -norm constraint inevitably produces dictionary atoms that are negatively correlated with the original signal; meanwhile, when we use a sparse linear combination of dictionary atoms to represent a signal, it is suboptimal for the dictionary atoms to “cancel each other out” by addition and subtraction to approximate the sample. In this paper, we propose a non-negative constrained dictionary learning (NCDL) algorithm to improve the reconstruction performance of CS with electrocardiogram (ECG) signals. Approach. Non-NCDL was divided into an encoding stage and a dictionary learning stage. In the encoding stage, non-negative constraints were imposed on the encoding coefficients and obtained the sparse solution using the alternating direction method of multipliers. At the same time, a penalty term was integrated into the objective function in order to remove small coding coefficients and achieve the effect of sparse coding. In the dictionary learning stage, the block coordinate descent algorithm was utilized to update the dictionary with a view to obtaining an overcomplete dictionary. Results. The performance of the proposed NCDL algorithm was evaluated using the standard MIT-BIH database. Quantitative performance metrics, such as percent root mean square difference (PRD1) and root mean square error, were compared with existing CS approaches to quantify the efficacy of the proposed scheme. For a PRD1 value of 9%, the compression ratio (CR) of the NCDL approach was around 2.78. When CR ranged from 1.05 to 2.78, the proposed NCDL approach outperformed the method of optimal direction, k-means singular value decomposition, and online dictionary learning approaches in ECG signal reconstruction based on CS. Significance. This promising preliminary result demonstrates the capability and feasibility of the proposed bioimpedance method and may open up a new direction for this application. The non-NCDL method proposed in this paper can be used to obtain a sparse basis and improve the performance of CS reconstruction.