Purpose: Recent studies have witnessed that self-attention modules can better solve the vision understanding problems by capturing long-range dependencies. However, there are very few works designing a lightweight self-attention module to improve the quality of MRI reconstruction. Furthermore, it can be observed that several important self-attention modules (e.g., the non-local block) cause high computational complexity and need a huge number of GPU memory when the size of the input feature is large. The purpose of this study is to design a lightweight yet effective spatial orthogonal attention module (SOAM) to capture long-range dependencies, and develop a novel spatial orthogonal attention generative adversarial network, termed as SOGAN, to achieve more accurate MRI reconstruction. Methods: We first develop a lightweight SOAM, which can generate two small attention maps to effectively aggregate the long-range contextual information in vertical and horizontal directions, respectively. Then, we embed the proposed SOAMs into the concatenated convolutional autoencoders to form the generator of the proposed SOGAN. Results: The experimental results demonstrate that the proposed SOAMs improve the quality of the reconstructed MR images effectively by capturing long-range dependencies. Besides, compared with state-of-the-art deep learning-based CS-MRI methods, the proposed SOGAN reconstructs MR images more accurately, but with fewer model parameters. Conclusions: The proposed SOAM is a lightweight yet effective self-attention module to capture long-range dependencies, thus, can improve the quality of MRI reconstruction to a large extent. Besides, with the help of SOAMs, the proposed SOGAN outperforms the state-of-the-art deep learning-based CS-MRI methods.
The problem of estimating rapidly time-varying channels is considered to be one of the key challenges in high mobility orthogonal frequency division multiplexing (OFDM) systems. In such scenarios, fast time variation within OFDM symbol duration requires overloaded measurements for estimation. By exploiting the inherent sparsity of wireless channels, the authors cast the channel estimation as a compressive sensing (CS) problem to reduce the required pilot symbols. Different from the existing CS-based estimators which mainly focus on the diagonal matrix model and treat the inter-carrier interference as additive noise, the proposed methods are designed for the non-diagonal matrix, a more precise representation of fast fading channels. To handle this more complex channel model, an iterative estimation scheme is presented, which adopts the recently introduced modified-CS algorithm. In addition, a more simplified scheme is also designed by utilising a reasonable approximation of the system model. Compared to the former method, it has a reduced computational complexity with limited performance degradation. The simulation results demonstrate that the two proposed CS-based methods are robust to large Doppler spreading and have better performance than conventional CS-based estimators for fast time-varying channels in OFDM systems.
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