基于曲波变换的航空瞬变电磁去噪

Airborne Transient Electromagnetic Noise Reduction Based on Curvelet Transform

噪声干扰严重影响着航空瞬变电磁的数据处理和成像解释,如何有效去噪成为航空瞬变电磁研究的重要内容。根据航空瞬变电磁噪声特点,结合曲波变换多尺度性,采用第二代快速离散曲波变换(FDCT),对航空瞬变电磁实测数据进行重构和去噪。首先建立带有异常体的三维理论模型,采用直接时间域瞬变电磁三维模拟程序进行正演;然后对理论电磁响应数据添加3种不同噪声(随机噪声、方波噪声、工业噪声),通过曲波变换和重构,生成不同尺度的图像,低尺度反映大的背景场,高尺度反映局部细节或者高频噪声。通过信噪比和相对误差等参数,对重构后的数据进行去噪效果评估。最后将该方法应用到航空瞬变电磁实测数据中,并与其他3种传统去噪方法(中值滤波、奇异值分解、小波变换)进行对比。结果表明:对于含有随机噪声和工业噪声的原始数据,去噪后的相对误差在2.6%以下;对于含有方波噪声的原始数据,去噪后的相对误差在6.5%以下,信噪比也高于传统去噪方法,证明第二代曲波变换可应用于航空瞬变电磁的数据去噪处理。

Noise interference seriously affects the data processing and imaging interpretation of aviation transient electromagnetic,and how to effectively denoise has become an important content of aviation transient electromagnetic research.Based on the characteristics of aviation transient electromagnetic noise and the multi-scale characteristics of curvelet transform,the second generation fast discrete curvelet transform(FDCT) was used to reconstruct and denoise actual aviation transient electromagnetic data.Firstly,a 3D theoretical model with anomalous bodies was established,and a direct time domain transient electromagnetic 3D simulation program was used for forward modeling.Then,three different types of noise,including random noise,square wave noise and industrial noise,were added to the theoretical electromagnetic response data,and images of different scales were generated through curvelet transform and reconstruction.Low scales reflect large background fields,while high scales reflect local details or high-frequency noise.Thirdly,the denoising effect of the reconstructed data was evaluated through parameters such as signal-to-noise ratio and relative error.Finally,the method was applied to the measured data of aviation transient electromagnetic and compared with several traditional denoising methods,including median filtering,singular value decomposition and wavelet transform.The results show that for the original data with random noise and industrial noise,the relative error after noise reduction is below 2.6%;for the original data with square wave noise,the relative error after noise reduction is below 6.5%,and the signal-to-noise ratio is also higher than traditional denoising methods,proving that the second generation curvelet transform can be applied to noise reduction of airborne transient electromagnetic data.