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Reducing the acquisition time for two-dimensional nuclear magnetic resonance (2D NMR) spectra is important. One way to achieve this goal is reducing the acquired data. In this paper, within the framework of compressed sensing, we proposed to undersample the data in the indirect dimension for a type of self-sparse 2D NMR spectra, that is, only a few meaningful spectral peaks occupy partial locations, while the rest of locations have very small or even no peaks. The spectrum is reconstructed by enforcing its sparsity in an identity matrix domain with ℓ(p) (p = 0.5) norm optimization algorithm. Both theoretical analysis and simulation results show that the proposed method can reduce the reconstruction errors compared with the wavelet-based ℓ(1) norm optimization.

Reconstruction of Self-Sparse 2D NMR Spectra from Undersampled Data in the Indirect Dimension