In the process of separating blended data, conventional methods based on sparse inversion assume that the primary source is coherent and the secondary source is randomized. The L1-norm, the commonly used regularization term, uses a global threshold to process the sparse spectrum in the transform domain; however, when the threshold is relatively high, more high-frequency information from the primary source will be lost. For this reason, we analyze the generation principle of blended data based on the convolution theory and then conclude that the blended data is only randomly distributed in the spatial domain. Taking the slope-constrained frequency-wavenumber ( f- k) transform as an example, we propose a frequency-dependent threshold, which reduces the high-frequency loss during the deblending process. Then we propose to use a structure weighted threshold in which the energy from the primary source is concentrated along the wavenumber direction. The combination of frequency and structure-weighted thresholds effectively improves the deblending performance. Model and field data show that the proposed frequency-structure weighted threshold has better frequency preservation than the global threshold. The weighted threshold can better retain the high-frequency information of the primary source, and the similarity between other frequency-band data and the unblended data has been improved.
Sparse inversion method of T2 spectrum based on the L1 norm for low-field nuclear magnetic resonance
