The low-rankness property of the Hankel matrix formulated from the clean seismic data corresponding to a few number of linear events has been successively leveraged in many low-rank (LR) approximation methods for seismic data denoising. The common scheme in these rank-reduction methods is to compute the best LR approximation of the formulated Hankel matrix and then obtain the denoised data from the LR matrix. However, without utilizing the Hankel structure when computing the LR approximation, if we rearrange the denoised data into a Hankel matrix, it is in general not exactly LR as expected. In this paper, we propose a Hankel LR (HLR) approximation method to simultaneously exploit both the Hankel structure and the LR property underlying the clean seismic data. The formulated HLR approximation problem is solved by an alternating-minimization-based algorithm. We provide rigorously convergence analysis of the proposed algorithm. The superior performance of the proposed HLR approximation method is demonstrated on both synthetic and field seismic data.

Coherent noise often interferes with synthetic aperture radar (SAR), which has a huge impact on subsequent processing and analysis. This paper puts forward a novel algorithm involving the convolutional neural network (CNN) and guided filtering for SAR image denoising, which combines the advantages of model-based optimization and discriminant learning and considers how to obtain the best image information and improve the resolution of the images. The advantages of proposed method are that, firstly, an SAR image is filtered via five different level denoisers to obtain five denoised images, in which the efficient and effective CNN denoiser prior is employed. Later, a guided filtering-based fusion algorithm is used to integrate the five denoised images into a final denoised image. The experimental results indicate that the algorithm cannot eliminate noise, but it does improve the visual effect of the image significantly, allowing it to outperform some recent denoising methods in this field.

As speckle seriously restricts the applications of remote sensing images in many fields, the ability to efficiently and effectively suppress speckle in a coherent imaging system is indispensable. In order to overcome the over-smoothing problem caused by the speckle suppression algorithm based on classical sparse representation, we propose a non-local speckle suppression algorithm that combines the non-local prior knowledge of the image into the sparse representation. The proposed algorithm first applies shearlet to sparsely represent the input image. We then incorporate the non-local priors as constraints into the image sparse representation de-noising problem. The denoised image is obtained by utilizing an alternating minimization algorithm to solve the corresponding constrained de-noising problem. The experimental results show that the proposed algorithm can not only significantly remove speckle noise, but also improve the visual effect and retain the texture information of the image better.

Seismic data reconstruction and denoising play a fundamental role in most seismic data processing algorithms which are often designed for regularly sampled and reliable data. By using the fact that the (block) Hankel matrix formulated from clean seismic data is low-rank if it corresponds to a few linear events, the low-rank based approach has been successfully used for seismic data reconstruction and denoising. In this paper, we simultaneously exploit the Hankel and low-rank structures within the (block) Hankel matrices of the clear and complete seismic data and formulate the problem of seismic data reconstruction and denoising as a Hankel low-rank reconstruction problem. The additional Hankel structure can further improve the performance for reconstruction and denoising. We then propose an iterative algorithm for solving the corresponding Hankel low-rank reconstruction problem. The algorithm is based on the alternating direction method of multipliers (ADMM) and has closed-form solutions for each update. Experiments on both synthetical and real seismic data demonstrate the superior performance of the proposed algorithm compared with conventional low-rank based methods for simultaneous seismic data reconstruction and denoising.