Reconstructing airborne gravity gradient (AGG) components will improve the signal-to-noise ratio by extracting the coherent signal. Fourier transformations are routinely used to reconstruct a consistent multicomponent AGG data set for noise suppression purposes. The crucial step is calculating the potential from multicomponent data based on the Fourier transform. Given that solving a least-squares (LS) problem is involved in most cases, the methods based on the Fourier transform have no essential difference. However, existing methods ignore the different noise levels of the components. To tackle this problem, we have used a weighted LS method instead and adopted a general expression for calculating the potential from multicomponent data corrupted by noise. With the wavenumber shift technique, this expression, used for AGG reconstruction, achieves the highest accuracy in theory. We finally develop a practical procedure for raw AGG data reconstruction that iteratively evaluates the noise level by updating the weights. In addition, we examine the errors within denoised data, and an improved simulation is adopted to estimate the statistics of noise levels and residual errors after denoising. We evaluate the effectiveness of our approach through synthetic examples, and the results find the ability of noise removal and estimation for data containing noise.
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