Fourier-based deconvolution (FoD) techniques, such as modulation transfer function compensation, are commonly employed in remote sensing. However, the noise is strongly amplified by FoD and is colored, thus producing poor visual quality. We propose an adaptive wavelet-based deconvolution algorithm for remote sensing called wavelet denoise after Laplacian-regularized deconvolution (WDALRD) to overcome the colored noise and to preserve the textures of the restored image. This algorithm adaptively denoises the FoD result on a wavelet basis. The term "adaptive" means that the wavelet-based denoising procedure requires no parameter to be estimated or empirically set, and thus the inhomogeneous Laplacian prior and the Jeffreys hyperprior are proposed. Maximum a posteriori estimation based on such a prior and hyperprior leads us to an adaptive and efficient nonlinear thresholding estimator, and therefore WDALRD is computationally inexpensive and fast. Experimentally, textures and edges of the restored image are well preserved and sharp, while the homogeneous regions remain noise free, so WDALRD gives satisfactory visual quality.
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