Sparsity & Compressed Sensing
Feng Huang1, Dong Han2, Xinlin Zhang3, Aiqi Sun4, and Xiaobo Qu3
1Neusoft Medical Systems, United States, 2Neusoft Medical Systems, Shenyang, China, 3Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, China, 4Neusoft Medical Systems, Shanghai, China

Synopsis

Compressed sensing (CS) is a powerful signal processing technique for reconstructing data from highly undersampled measurements. The introduction of CS to magnetic resonance imaging (MRI) has dramatically reduced scan acquisition time, and has demonstrated great success in diverse applications over the last decade. In this talk, we will cover the basic theory of CS, and then give an overview of the combination of CS with fast imaging approaches, such as parallel imaging and partial Fourier. Furthermore, we will also introduce the advanced CS techniques combined with deep learning.

Target Audience

Physicists and engineers who wish to acquire a better understanding of advanced magnetic resonance image reconstruction methods based on compressed sensing (CS).

Objectives

- To develop a basic understanding of compressed sensing theory
- To provide an overview of the combination of compressed sensing with fast imaging approaches
- To introduce the advanced compressed sensing techniques combined with deep learning

Contents

Part I：CS Theory
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. The introduction of CS into MRI field dramatically improve the acquisition efficiency. Hence, all major vendors have developed CS in their systems. The development of CS in MRI requires 3 key elements:
1. Transform Sparsity: The image must have a sparse representation in a transform domain.
2. Incoherence of Undersampling Artifacts: The aliasing artifacts introduced by k-space undersampling must be noise-like in the transform domain and can be removed by enforcing sparsity.
3. Nonlinear Reconstruction: The image must be reconstructed with a nonlinear algorithm to enforce sparsity and keep the consistency of the acquired samples with the reconstructed image.
Accordingly, research on CS mainly focus on these three aspects: (a) constructing an optimal sparse representation [1-8]; (b) designing an optimal undersampling pattern [9-13]; and (c) designing an effective algorithm [14-17].

Part II：CS with Parallel Imaging and Partial Fourier
CS, parallel imaging (PI), and Partial Fourier are all fast imaging techniques, but based on different principle. Therefore, it is natural to combine them and achieve faster acquisition. Nowadays, most commercialized CS techniques are actually the combination of these three techniques. These methods can be combined either sequentially or jointly. Both combination schemes will be introduced and compared in this talk [18-26].

Part III：CS with Deep Learning
Recently, deep learning has become the research hotspot in many technical fields, and its effectiveness in MRI applications has been demonstrated by many research papers and technical reports [27-33]. Great progress has been made in the application of deep learning to MRI, from brute-force domain-transform manifold learning [34] to more interpretable model-based approaches [35], from image-domain de-noising [36] and de-aliasing [37] to hybrid-domain image reconstruction [38]. In this talk, we will first elaborate the mathematical foundations of deep learning and its strength of modeling complex non-linear transformations. Then, the combination of CS and deep learning will be introduced with special emphasis on the unrolling of traditional CS iterative methods using neural networks, which has become the mainstream of DL-based MR imaging researches [39-44]. Furthermore, this talk will also point out some pitfalls and challenges of current DL-based approaches from industrial perspective, and present several future directions for both academic and industrial societies.

Acknowledgements

No acknowledgement found.

References

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Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)