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Image rain removal is an essential problem of common concern in the fields of image processing and computer vision. Existing methods have resorted to deep learning techniques to separate rain streaks from the background by leveraging some prior knowledge. However, the mismatch between the size of the rain streaks during the training and testing phases, especially when large rain streaks are present, frequently leads to unsatisfactory deraining results. To address this issue, we propose a multi-scale self-calibrated dual attention lightweight residual dense deraining network (MDARNet) for better deraining performance. Specifically, the network consists of monogenic wavelet transform-like hierarchy and self-calibrated dual attention mechanism. With the help of scale-space properties of the monogenic wavelet transform, key features at different scales can be extracted at the same location, which makes it easier to match structural features across scales. The self-calibrated double attention mechanism was used as a basic model for enhancing the channel dependence and spatial correlation between each layer component of the monogenic wavelet transform. Thus, the network can establish long-range dependencies and take advantage of rich contextual information and multi-scale redundancy to accommodate rain streaks of different shapes and sizes. Experiments on synthetic and real image datasets show that the method outperforms many of the latest single-image deraining methods in terms of visual and quantitative metrics. The source code can be obtained from https://github.com/smart-hzw/MDARNet.