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.

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their undersampled Fourier coefficients using infimal convolution regularizations. The image is modeled as the superposition of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low-rank property of the matrices to formulate a combined regularized optimization problem. In order to solve the problem efficiently and to avoid the high-memory demand resulting from the large-scale Toeplitz matrices, we introduce a fast and a memory-efficient algorithm based on the half-circulant approximation of the Toeplitz matrix. We demonstrate our algorithm in the context of single and multi-channel MR images recovery. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the state-of-the-art approaches.

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.