The existing remote sensing (RS) image dehazing methods based on deep learning have sought help from the convolutional frameworks. Nevertheless, the inherent limitations of convolution, i.e ., local receptive fields and independent input elements, curtail the network from learning the long-range dependencies and non-uniform distributions. To this end, we design an effective RS image dehazing Transformer architecture, denoted as RSDformer. Firstly, given the irregular shapes and non-uniform distributions of haze in RS images, capturing both local and non-local features is crucial for RS image dehazing models. Hence, we propose a detail-compensated transposed attention to extract the global and local dependencies across channels. Secondly, to enhance the ability to learn degraded features and better guide the restoration process, we develop a dual-frequency adaptive block with dynamic filters. Finally, a dynamic gated fusion block is designed to achieve fuse and exchange features across different scales effectively. In this way, the model exhibits robust capabilities to capture dependencies from both global and local areas, resulting in improving image content recovery. Extensive experiments prove that the proposed method obtains more appealing performances against other competitive methods.

An accurate frequency estimator of complex sinusoid in additive white noise is proposed. It is based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT). Zero-padding is firstly performed before the FFT of the sinusoid sampled data, and the coarse estimate is obtained by searching the discrete frequency index of the maximum FFT spectrum line. Then the fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values located on the left and right side of the maximum spectrum line. The correlation coefficients between the Fourier Transform of the noises on two arbitrarily spaced spectrum lines are derived, and the MSE calculation formula is derived in additive white noise background based on the correlation coefficients. Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.

An accurate frequency estimator for real sinusoid based on Discrete Fourier Transform (DFT) is proposed. The proposed estimator is based on the interpolation of the maximum DFT spectral line and two Discrete-Time Fourier Transform (DTFT) spectral lines and can operate with both the rectangular window and the maximum sidelobe decay (MSD) window. In the coarse estimation step, the proposed estimator with the MSD window is used. According to the value of the coarse estimate, the negative frequency spectral component is removed. In the fine estimation step, the proposed estimator with the rectangular window is utilized to achieve the Cramer–Rao lower bound (CRLB). Simulation results show that the performance of this algorithm is better than that of the AM algorithm, Candan algorithm, Djukanovic algorithm, and FDIAM algorithm.

An accurate frequency estimation method of multi-component sinusoidal signal in additive white Gaussian noise (AWGN) is proposed. The algorithm is implemented in the frequency domain and based on discrete Fourier transform (DFT). The maximum DFT spectral line and two Discrete-Time Fourier Transform (DTFT) samples located on the same side of the maximum DFT spectral line are used to estimate the frequency of a sinusoidal component. And this algorithm is utilized in both the coarse estimation and the fine estimation. Simulation results show that compared with the competing estimators, the presented method is closer to the Cramer-Rao lower bound (CRLB). And it is almost independent of the frequency displacement. The numerical complexity of the presented method is similar with the competing DFT-based algorithms.

A sinusoidal frequency estimator based on interpolated Discrete Fourier Transform (DFT) algorithm by using Maximum Sidelobe Decay (MSD) windows is proposed in this paper. Firstly, the received sinusoid is weighted by an appropriate MSD window. Then DFT is carried out on the weighted sinusoid and the coarse estimation is acquired by finding the position of the maximum DFT sample. Different from all the existing algorithms, the presented estimator adopts the maximum DFT sample and two Discrete Time Fourier Transform (DTFT) spectral lines which are on the same side of the maximum DFT sample in the fine estimation step. MSE formulas of the presented estimator in additive white noise are derived. Simulation results indicate that the presented estimator outperforms the competing estimators.