Highly undersampled schemes in magnetic resonance fingerprinting (MRF) typically lead to aliasing artifacts in reconstructed images, thereby reducing quantitative imaging accuracy. Existing studies mainly focus on improving the reconstruction quality by incorporating temporal or spatial data priors. However, these methods seldom exploit the underlying MRF data structure driven by imaging physics and usually suffer from high computational complexity due to the high-dimensional nature of MRF data. In addition, data priors constructed in a pixel-wise manner struggle to incorporate non-local and non-linear correlations. To address these issues, we introduce a novel MRF reconstruction framework based on the graph embedding framework, exploiting non-linear and non-local redundancies in MRF data. Our work remodels MRF data and parameter maps as graph nodes, redefining the MRF reconstruction problem as a structure-preserved graph embedding problem. Furthermore, we propose a novel scheme for accurately estimating the underlying graph structure, demonstrating that the parameter nodes inherently form a low-dimensional representation of the high-dimensional MRF data nodes. The reconstruction framework is then built by preserving the intrinsic graph structure between MRF data nodes and parameter nodes and extended to exploiting the globality of graph structure. Our approach integrates the MRF data recovery and parameter map estimation into a single optimization problem, facilitating reconstructions geared toward quantitative accuracy. Moreover, by introducing graph representation, our methods substantially reduce the computational complexity, with the computational cost showing a minimal increase as the data acquisition length grows. Experiments show that the proposed method can reconstruct high-quality MRF data and multiple parameter maps within reduced computational time.

Detection of infrared dim and small targets with diverse and cluttered background plays a significant role in many applications. In this paper, we propose a deep low-rank and sparse patch-image network, termed as Deep-LSP-Net, to effectively detect small targets in a single infrared image. Specifically, by using the local patch construction scheme, we first transform the original infrared image into a patch-image, which can be decomposed as a superposition of the low-rank background component and the sparse target component. The target detection is thus formulated as an optimization problem with low-rank and sparse regularizations, which can be solved by the alternating direction method of multipliers (ADMM). We unroll the iterative algorithm into deep neural networks, where a generalized sparsifying transform and a singular value thresholding operator are learned by the convolutional neural networks (CNNs) to avoid tedious parameter tuning and improve the interpretability of the neural networks. We conduct comprehensive experiments on two public datasets. Both qualitative and quantitative experimental results demonstrate that the proposed algorithm can obtain improved performance in small infrared target detection compared with state-of-the-art algorithms.

Magnetic resonance fingerprinting (MRF) can rapidly perform simultaneous imaging of multiple tissue parameters. However, the rapid acquisition schemes used in MRF inevitably introduce aliasing artifacts in the recovered tissue fingerprints, reducing the accuracy of the predicted parameter maps. Current regularized reconstruction methods are based on iterative procedures which are usually time-consuming. In addition, most of the current deep learning-based methods for MRF often lack interpretability owing to the black-box nature, and most deep learning-based methods are not applicable for non-Cartesian scenarios, which limits the practical applications. In this paper, we propose a joint reconstruction model incorporating MRF-physics prior and the data correlation constraint for non-Cartesian MRF reconstruction. To avoid time-consuming iterative procedures, we unroll the reconstruction model into a deep neural network. Specifically, we propose a learned CANDECOMP/PARAFAC (CP) decomposition module to exploit the tensor low-rank priors of high-dimensional MRF data, which avoids computationally burdensome singular value decomposition. Inspired by the MRF-physics, we also propose a Bloch response manifold module to learn the mapping between reconstructed MRF data and the multiple parameter maps. Numerical experiments show that the proposed network can reconstruct high-quality MRF data and multiple parameter maps within significantly reduced computational time.

Due to the capability of fast multiparametric quantitative imaging, magnetic resonance fingerprinting (MRF) is becoming a promising quantitative magnetic resonance imaging approach. However, the artifacts caused by the highly undersampled data acquisition lead to inaccurate estimation of the tissue parameter maps. Based on the assumption that the 3-D MRF data can be modeled as a piecewise smooth signal, with the discontinuities localized to the zero sets of a bandlimited function, we exploit the low-rank property of the structured Toeplitz matrix constructed from the Fourier measurements. In addition, we adopt the subspace projection scheme to improve the accuracy of parameter estimation. In order to efficiently solve the regularized problem, we propose an iterative two-stage algorithm, which alternately updates the k -space data and projects the space-time matrix into the dictionary space. Numerical experiments demonstrate that the proposed algorithm shows significant improvement in MRF time-series images reconstruction and can provide more accurate parameter maps over the state-of-the-art algorithms.