Seismic interpolation can provide complete data for some multichannel processing techniques such as time lapse imaging and wave equation migration. However, field seismic data often contains random noise and noisy data interpolation is a challenging task. A traditional method applies interpolation and denoising separately, but this needs two workflows. Simultaneous interpolation and denoising combines interpolation and denoising in one workflow and can also get acceptable results. Most existing interpolation methods can only recover missing traces but fail to attenuate noise in sampled traces. In this study, a novel thresholding strategy is proposed to remove the noise in the sampled traces and meanwhile recover missing traces during interpolation. For each iteration, the residual is multiplied by a weighting factor and then added to the iterative solution, after which the sum in the transformed domain is calculated using the thresholding operation to update the iterative solution. To ensure that the interpolation and denoising results are robust, the exponential method was chosen to reduce the threshold values in small quantities. The curvelet transform was used as sparse representation and three interpolation methods were chosen as benchmarks. Three numerical tests results proved the effectiveness of the proposed method on removing noise in the sampled traces when the minimum threshold values are correctly chosen.

地震插值可以为某些多通道处理技术（例如延时成像和波动方程偏移）提供完整的数据。但是，现场地震数据通常包含随机噪声，而噪声数据插值是一项艰巨的任务。传统方法分别应用插值和去噪，但这需要两个工作流程。同时插值和去噪在一个工作流程中结合了插值和去噪，也可以获得可接受的结果。大多数现有的插值方法只能恢复丢失的迹线，但不能衰减采样迹线中的噪声。在这项研究中，提出了一种新颖的阈值处理策略，以消除采样轨迹中的噪声，同时在插值过程中恢复丢失的轨迹。对于每次迭代，残差乘以加权因子，然后添加到迭代解中，然后使用阈值运算来计算变换域中的总和以更新迭代解。为了确保内插和去噪结果的鲁棒性，选择了指数方法来少量减少阈值。将Curvelet变换用作稀疏表示，并选择了三种插值方法作为基准。三个数值测试结果证明，当正确选择最小阈值时，该方法可以有效消除采样迹线中的噪声。为了确保内插和去噪结果的鲁棒性，选择了指数方法来少量减少阈值。将Curvelet变换用作稀疏表示，并选择了三种插值方法作为基准。三个数值测试结果证明，当正确选择最小阈值时，该方法可以有效消除采样迹线中的噪声。为了确保内插和去噪结果的鲁棒性，选择了指数方法来少量减少阈值。将Curvelet变换用作稀疏表示，并选择了三种插值方法作为基准。三个数值测试结果证明，当正确选择最小阈值时，该方法可以有效消除采样迹线中的噪声。