In this paper, the deep learning (DL) approach is applied to a joint training scheme for asynchronous motor imagery-based Brain-Computer Interface (BCI). The proposed DL approach is a cascade of one-dimensional convolutional neural networks and fully-connected neural networks (CNN-FC). The focus is mainly on three types of brain responses: non-imagery EEG (\textit{background EEG}), (\textit{pure imagery}) EEG, and EEG during the transitional period between background EEG and pure imagery (\textit{transitional imagery}). The study of transitional imagery signals should provide greater insight into real-world scenarios. It may be inferred that pure imagery and transitional EEG are high and low power EEG imagery, respectively. Moreover, the results from the CNN-FC are compared to the conventional approach for motor imagery-BCI, namely the common spatial pattern (CSP) for feature extraction and support vector machine (SVM) for classification (CSP-SVM). Under a joint training scheme, pure and transitional imagery are treated as the same class, while background EEG is another class. Ten-fold cross-validation is used to evaluate whether the joint training scheme significantly improves the performance task of classifying pure and transitional imagery signals from background EEG. Using sparse of just a few electrode channels ($C_{z}$, $C_{3}$ and $C_{4}$), mean accuracy reaches 71.52 % and 70.27 % for CNN-FC and CSP-SVM, respectively. On the other hand, mean accuracy without the joint training scheme achieve only 62.68 % and 52.41 % for CNN-FC and CSP-SVM, respectively.