Cortico-muscular interactions play important role in sensorimotor control during motor task and are commonly studied by cortico-muscular coherence (CMC) method using joint electroencephalogram-surface electromyogram (EEG-sEMG) signals. As noise and time delay between the two signals weaken the CMC value, coupling difference between non-task sEMG channels is often undetectable. We used sparse representation of EEG channels to compute CMC and detect coupling for task-related and non-task sEMG signals. High-density joint EEG-sEMG (53 EEG channels, 4 sEMG bipolar channels) signals were acquired from 15 subjects (30.26 ± 4.96 years) during four specific hand and foot contraction tasks (2 dynamic and 2 static contraction). Sparse representations method was applied to detect projection of EEG signals on each sEMG channel. Bayesian optimization was employed to select best-fitted method with tuned hyperparameters on the input feeding data while using 80% data as the train set and 20% as test set. K-fold (K = 5) cross-validation method was used for evaluation of trained model. Two models were trained separately, one for CMC data and the other from sparse representation of EEG channels on each sEMG channel. Sensitivity, specificity, and accuracy criteria were obtained for test dataset to evaluate the performance of task-related and non-task sEMG channels detection. Coupling values were significantly different between grand average of task-related compared to the non-task sEMG channels (Z = -6.33, p< 0.001, task-related median = 2.011, non-task median = 0.112). Strong coupling index was found even in single trial analysis. Sparse representation approach (best fitted model: SVM, Accuracy = 88.12%, Sensitivity = 83.85%, Specificity = 92.45%) outperformed CMC method (best fitted model: KNN, Accuracy = 50.83%, Sensitivity = 52.17%, Specificity = 49.47%). Sparse representation approach offers high performance to detect CMC for discerning the EMG channels involved in the contraction tasks and non-tasks.