Fig. 1

(a) Different distributions of decaying factors, and the corresponding decay signals (b) linear scale (c) logarithmic scale

Fig. 2

DOSY spectra with two diffusion components: (a) without peak overlap, (b) with peak overlap; and corresponding experimental signals: (c) without peak overlap, (b) with peak overlap

Fig. 3

The DOSY experimental data of two samples (a) QGC (containing quinine, geraniol, and camphene) (b) GSP (containing glucose, sucrose, and PEG 600)

Table 1

The convergence of SCORE with different P

Fig. 4

Separated spectra of SCORE on a three-component-mixture GSP. (a1)~(a5) the spectra of 5 components when P is set to 5; (b1)~(b8) the spectra of 8 components when P is set to 8. Red color denotes the ineffective components

Fig. 5

Reconstructed DOSY spectra of QGC mixture with different algorithms[44]. (a) Univariate mono-exponential fitting; (b) SILT; (c) LRSpILT

Fig. 6

Reconstructed DOSY spectra of GSP mixture with different algorithms[45]. (a) LRSpILT; (b) SCORE; (c) CoMeF; (d), (e), (f): Zoom-in regions

Fig. 7

Training procedures of the neural network for Laplace NMR data processing

Fig. 8

T2 distribution results of different algorithms under different SNR conditions[53]. Red solid lines denote the ground truth, red dashed lines are the results of classic algorithm BRD, and black dashed lines represent results of ATT-CNN

Fig. 9

DOSY spectral reconstruction based on simplified Transformer. (a) Framework; (b) Function of the encoding module

Fig. 10

Reconstructed results of M6 with different algorithms[54]. (a) LRSpILT; (b) CoMeF; (c) DRECT

Table 2

Regularization parameter settings of classic methods on three samples, and the computation efficiency comparison with DRECT