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Abstract Deep learning-based approaches have demonstrated impressive performance in single-image super-resolution (SISR). Efficient super-resolution compromises the reconstructed image’s quality to have fewer parameters and Flops. Ensured efficiency in image reconstruction and improved reconstruction quality of the model are significant challenges. This paper proposes a trio branch module (TBM) based on structural reparameterization. TBM achieves equivalence transformation through structural reparameterization operations, which use a complex network structure in the training phase and convert it to a more lightweight structure in the inference, achieving efficient inference while maintaining accuracy. Based on the TBM, we further design a lightweight version of the enhanced spatial attention mini (ESA-mini) and the residual trio feature block (RTFB). Moreover, the multiple RTFBs are combined to construct the residual trio network (RTFN). Finally, we introduce a localized contrast loss for better applicability to the super-resolution task, which enhances the reconstruction quality of the super-resolution model. Experiments show that the RTFN framework proposed in this paper outperforms other state-of-the-art efficient super-resolution methods in terms of inference speed and reconstruction quality.

Deep learning models, such as recurrent neural network (RNN) models, are suitable for modeling and forecasting non-stationary time series but are not interpretable. A prediction model with interpretability and high accuracy can improve decision makers’ trust in the model and provide a basis for decision making. This paper proposes a double decomposition strategy based on wavelet decomposition (WD) and empirical mode decomposition (EMD). We construct a prediction model of high-order fuzzy cognitive maps (HFCM), called the WE-HFCM model, which considers interpretability and strong reasoning ability. Specifically, we use the WD and EDM algorithms to decompose the time sequence signal and realize the depth extraction of the signal’s high-frequency, low-frequency, time-domain, and frequency domain features. Then, the ridge regression algorithm is used to learn the HFCM weight vector to achieve modeling prediction. Finally, we apply the proposed WE-HFCM model to stationary and non-stationary datasets in simulation experiments. We compare the predicted results with the autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) models.For stationary time series, the prediction accuracy of the WE-HFCM model is about 45% higher than that of the ARIMA, about 35% higher than that of the SARIMA model, and about 16% higher than that of the LSTM model. For non-stationary time series, the prediction accuracy of the WE-HFCM model is 69% higher than that of the ARIMA and SARIMA models.