磁共振指纹成像（Magnetic Resonance Fingerprinting，MRf）是一种快速高效的定量成像技术。它采用伪随机变化的脉冲激发序列编码组织信号，并通过指纹重建与参数反演实现定量成像。现有模型类MRf重建方法假设图像在某变换域是稀疏的，并通过引入稀疏约束来抑制折叠伪影的干扰，提高参数估计的准确率。然而，考虑到图像块内容的多样性，固定稀疏变换域无法获得最优的稀疏度，折叠噪声抑制效果有限，导致参数反演不准。基于盲压缩感知（Blind Compress Sensing，BCS）理论，本文将稀疏变换学习重建模型引入磁共振指纹成像模型，提出了一种融合自适应稀疏变换学习的磁共振指纹重建方法。该方法通过数据驱动的自适应学习，获得图像块的最佳稀疏变换域和最优稀疏度，改善折叠噪声的抑制效果，同时保护边缘特征；其次，利用磁共振指纹的字典重建指纹序列的时域特征，改善指纹的辨识度，保证参数反演的准确性；最后，为提高重建速度和反演速度，本文将指纹重建和参数反演过程均映射到低维子空间中，降低时域维度减少计算量。为了验证算法的有效性，仿真实验将本文算法与多种模型类重建算法进行比较。实验结果表明，相较于其它模型类重建算法，本文所提算法的参数估算准确性更高，三种定量参数的估计误差分别降低到：4.67%,、4.2%、 1.12%，仅为常规反演算法误差的30%。

Objective: Magnetic resonance fingerprinting (MRf) is a rapid and efficient quantitative imaging technique that can simultaneously provide multiple physiological tissue parameters. It encodes the tissue differences into a unique pattern of fingerprints using pseudo-random pulse excitation sequences. Through signal recovery and pattern recognition, the quantitative parameter maps can be obtained via fingerprint reconstruction and parameter inversion. Similar to the fast MR imaging techniques, non cartesian sparse sampling is utilized in MRf to accelerate the scanning process, allowing the entire field of view to be sampled within a single repetition time (TR). As we know, highly sparse downsampling can introduce significant aliasing noise in the reconstructed images which are used to generate fingerprint sequences. Reconstructing clean and distinctive fingerprints is crucial for bridging qualitative measurements with quantitative physiology tissue parameter maps in MRf technology. To remove aliasing noise, model-based reconstruction methods address this issue by solving optimization problems. To ensure the convergence of solutions, various constraints, such as low rank prior, sparsity prior, are applied to the optimization problem. However, due to the diversity of images, many of these prior constraints fail to adequately balance denoising and edge preserving. The low rank constraint focuses on noise suppression, which easily leads to oversmoothing of reconstructed fingerprints. Sparse constraint improves the oversmoothing problem to some extent. Considering the diversity of image blocks, the best sparse representation and reconstruction effect of signal cannot be achieved using fixed sparse transform and uniform sparsity level. In contrast, Blind Compress Sensing (BCS) adapts to learn the features and structures of the data without making any prior assumptions. Method: Based on above analysis, we propose an adaptive sparsifying transform learning based magnetic resonance fingerprinting reconstruction method. First, the images are reconstructed through iterative processes involving both sparsifying transform domain learning and sparse representation-based reconstruction. With the adaptively learned sparse transformation, lower sparse levels can be achieved, effectively removing aliasing artifacts compared to conventional sparsifying transforms such as wavelet or Fourier transform. Second, since the MRf dictionary serves as the ideal estimation of fingerprints, we can retrieve the temporal features of fingerprints by incorporating the MRf dictionary into the reconstruction model. In each iteration, the reconstructed fingerprints are updated with the best-matching dictionary atoms to improve the discrimination of fingerprints. Finally, to accelerate the reconstruction process, Singular Value Decomposition (SVD) is applied to compress the temporal dimension of fingerprints based on the correlation of signals at adjacent time points. Thus, the reconstruction process and dictionary matching are carried out in a subspace spanned by 5 to 10 singular components. To verify the effectiveness of our method, simulation experiments compare the proposed method with other state-of-art model-based reconstruction methods. Result: The reconstructed tissue parameter maps demonstrated that our method achieves higher accuracy than five other MRf reconstruction methods. The average relative errors of the three parameter maps reconstructed by our method are 4.67%, 4.2% and 1.12%, respectively. Compared to conventional MRf methods, the relative errors have been reduced by more than 50%. And it also has obvious improvement compared with other model-based methods without incurring additional computation time. Several key parameters are involved in our method, including block size, number of blocks, and the number of singular components. The optimal values for these parameters are determined through experiments. We also present the performance of our method with different values of these parameters in the discussion section. Conclusion: In this paper, we introduced an innovative adaptive sparsifying transform learning-based reconstruction method for magnetic resonance fingerprinting (MRf), enhancing the accuracy and quality of tissue parameter maps. Our approach effectively mitigates aliasing artifacts by leveraging the MRf dictionary and incorporates Singular Value Decomposition (SVD) to compress the temporal dimension without increasing computation time. The results indicate that our method outperforms other MRf reconstruction techniques. The research findings will contribute to the advancement of MRf technology towards the clinical applications, holding significant value in medical imaging, particularly in early disease detection and precision medicine. By improving image quality and the accuracy of parameter measurements, this approach aids clinicians in diagnosing lesions earlier and more accurately, optimizing treatment plans. However, the current algorithm still requires manual adjustment of iteration thresholds to achieve optimal sparsification effects when faced with different sampling trajectories. Future research will focus on achieving adaptive threshold selection to further enhance the versatility and practical application potential of the algorithm.