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A B S T R A C TSeismic data reconstruction, as a preconditioning process, is critical to the performance of subsequent data and imaging processing tasks. Often, seismic data are sparsely and non-uniformly sampled due to limitations of economic costs and field conditions. However, most reconstruction processing algorithms are designed for the ideal case of uniformly sampled data. In this paper, we propose the non-equispaced fast discrete curvelet transform-based three-dimensional reconstruction method that can handle and interpolate non-uniformly sampled data effectively along two spatial coordinates. In the procedure, the three-dimensional seismic data sets are organized in a sequence of two-dimensional time slices along the source-receiver domain. By introducing the two-dimensional non-equispaced fast Fourier transform in the conventional fast discrete curvelet transform, we formulate an L1 sparsity regularized problem to invert for the uniformly sampled curvelet coefficients from the non-uniformly sampled data. In order to improve the inversion algorithm efficiency, we employ the linearized Bregman method to solve the L1-norm minimization problem. Once the uniform curvelet coefficients are obtained, uniformly sampled three-dimensional seismic data can be reconstructed via the conventional inverse curvelet transform. The reconstructed results using both synthetic and real data demonstrate that the proposed method can reconstruct not only non-uniformly sampled and aliased data with missing traces, but also the subset of observed data on a non-uniform grid to a specified uniform grid along two spatial coordinates. Also, the results show that the simple linearized Bregman method is superior to the complex spectral projected gradient for L1 norm method in terms of reconstruction accuracy.

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Morphine is an opioid analgesic drug routinely used to treat pain in several medical conditions including cancer. Increasing evidence has shown that morphine can directly modulate cancer growth via regulating angiogenesis. In this work, we investigated the effect of morphine on angiogenesis under pathological conditions. We showed that morphine, in a concentration typical of that observed in patient's blood, stimulates tumour angiogenesis under serum deprivation and H2O2‐induced oxidative stress conditions. We found that morphine protected human lung tumour associated‐endothelial cell (HLT‐EC) against serum deprivation or H2O2‐induced inhibition of capillary network formation. Furthermore, morphine stimulated other biological functions of HLT‐EC under serum deprivation and H2O2‐induced pathological conditions, such as growth, migration and survival, without affecting HLT‐EC adhesion. Interestingly, morphine at the same concentration did not affect lung tumour cell growth and survival, suggesting the specific protective role of morphine at low micromolar concentrations on tumour angiogenesis. Using in vivo Matrigel angiogenesis assay, it was found that morphine stimulated in vivo angiogenesis under H2O2‐induced pathological condition. The opioid receptor antagonist, naloxone, did not inhibit the protective activity of morphine in in vivo angiogenesis, indicating that the effect was less likely to be mediated by the typical opioid receptors. Mechanism analysis indicated that morphine alleviated serum deprivation and H2O2‐induced angiogenesis inhibition via reducing oxidative stress and damage, and activating Akt/mTOR/eIF4E signalling. We demonstrate the protective role of morphine on tumour angiogenesis under pathological conditions. Our work suggests that clinical use of morphine may be harmful in patients with angiogenesis‐dependent cancers.

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