The role of granular computing in time series analysis is becoming increasingly important. Currently, there remains scope for enhancing the specificity of information description by information granules. To improve the specificity, a novel elliptical information granule is designed for time series similarity measurement in this paper. An elliptical information granule is defined by its centre and its long and short half-axes. Elliptical information granules can be constructed based on justifiability and specificity, guided by the principle of justifiable granularity. Multiple elliptical information granules are constructed using fuzzy C-means clustering and compactness principles. A time series similarity measurement method is then developed based on the geometric similarity of elliptical information granules. Experimental result shows that the constructed elliptical information granules provide a more specific information description compared to rectangular information granules, while offering significant advantages in time series similarity measurement. The proposed method has significant potential for time series analysis and modelling.

Matching multibeam echo sounder (MBES) data and side scan sonar (SSS) data has the potential to obtain high-accuracy seabed topography and geomorphological details simultaneously. However, the position uncertainty as well as radiometric and geometric distortion of SSS images bring serious challenges to the matching process. In this article, we proposed a novel matching method using sea bottom line matching and template matching to solve the above problems. First, we extracted the sea bottom points from the SSS image and calculated the depth series of the sea bottom line as the auxiliary information. Then, coarse matching is employed to this depth series and its corresponding terrain data of the MBES, to remove the coarse position uncertainty between the SSS and MBES images. After that, multiscale local self-similarity (MLSS) is proposed here, which is robust to geometric and radiometric distortion. Based on the coarse-matched SSS image, MLSS descriptor is applied for template matching between SSS and MBES images. Experiments verified the performance of the method. The high-resolution and high-accuracy seabed topography and surface details are eventually obtained.

The wide applications of 3-D sonar measurements are severely limited by factors such as water column interference, acoustic shadows, complex structures, and scattering noise. Outliers in 3-D sonar data are difficult to remove using traditional methods because the inference factors are different from other types of point cloud data. Therefore, this article presents a novel outlier filtering method by analyzing the sequential characteristics of the 3-D sonar data. First, the underwater point cloud is processed by super-voxel clustering method to decompose complex point cloud structures into several super-voxels with simple structures. Then we convert the point cloud data into subsequence data according to the surveying principle of 3-D sonar scanning and super-voxel results. After that, an anomaly score calculation and anomaly region determination method based on the rectangular information granulation of subsequence data is proposed. This method can capture the intrinsic changing characteristics of each subsequence and has a good recognition effect on the abnormal subsequence. Finally, an outlier detection method combining the Grubbs principle and the abnormal score is proposed and applied to the abnormal subsequences, which considers the distortion not only in the vertical direction but also in the horizontal direction. The experimental results show that the proposed comprehensive filtering method has good accuracy for both horizontal and vertical point cloud data. The average overall accuracy of the test results is 99.1%, and the average kappa coefficient is 0.88, which can be effectively applied to the 3-D sonar point cloud data filtering processing in complex underwater areas.

Sub-bottom profiler (SBP) Sonar data are always polluted by noise that leads to the wrong interpretation. To deal with this situation, a method combining the prior information of SBP sonar data and the variational mode decomposition (VMD) framework is proposed attempting to recover clean data from its corrupted version. First, to deal with the unknown mode number of VMD method, a mode number determination criterion which takes the frequency distribution characteristic into consideration has been proposed. Then, the sea bottom line is extracted using the enhancement filtering and the threshold extraction method. The echoes above the sea bottom are from the water column and mainly contain noise components. To determine which modes are caused by the noise, we obtained and analyzed these echoes to achieve the noise prior frequency feature. After that, the noise modes can be determined and removed using its prior frequency information. Both simulated and real experiments have been used to test the effectiveness of the proposed method, and good performance has been achieved.

The acquirement of seafloor small target information is one of the most important tasks of a side-scan sonar (SSS) survey. Thus, SSS small target detection becomes fundamental work for SSS applications which holds vital importance for marine engineering, maritime military and so on. However, existing methods cannot take the prior shadow information into consideration well, which would easily miss small targets. In this paper, a novel SSS small target detection method considering shadow characteristics is proposed. First, we give a detailed analysis of the SSS imaging theory as well as the prior information about the characteristics of shadows. Then, considering the prior information of the SSS short-shadow, the second partial derivative of the Gaussian function is specifically introduced for the construction of a weighted item. After that, incorporating the weighted item with thel21-norm,l1-norm, and low-rank constraints on the noise, the target, as well as the background, respectively, a weighted sparse detection model is proposed. To further take the long-shadows into consideration, a long-shadow detection method and its corresponding target detection method are proposed. By combining the two detection results, we get the comprehensive detection result. Experiments based on SSS images in different scenarios proved the validity of the proposed method.

Sediment classification based on Chirp sonar data is very important in support of marine science and engineering. The traditional adopted spectral-ratio (SR) method is widely applied for its theory of simplicity and easy employment. However, the performance of SR method is heavily degraded by spectrum vibrations introduced by overlapping reflections. To solve this problem, a reflection signal decomposition method is proposed in this paper, which decomposes the overlapping reflection into separate reflection sub-signals to avoid the spectrum vibration. Firstly, we re-derive the overlapping reflection expression from the convolution model and give the initial model for the decomposition of the Chirp sonar signal. Then, introducing the spectrum smooth prior into consideration and incorporating it with the fidelity and the bandwidth terms, the decomposition model with constraints is proposed. After that, an iterative algorithm is introduced to solve the model optimization problem. The reflection sub-signal can be well obtained. Finally, through a least square linear fitting for the logarithm of the spectral ratio (the log-SR) of reflection sub-signals, quality factor (Q) which is applied for sediment classification can finally be achieved. Both real and simulated experiments have been conducted to verify the proposed method and some meaningful discussions are also drawn.

The use of side-scan sonar (SSS) images is limited by radiometric distortion, which is affected by factors such as angle response, beam pattern, and incident energy. Traditional methods have overlooked the impact of sediment-dependent angle response, degrading performance in complex SSS images. In this study, we propose a method for correcting radiometric distortion on SSS images based on the variational Retinex framework and sediment characteristics. First, we analyze the imaging theory of SSS and the angle responses of various sediments. We introduce a mixed Gaussian model to describe the feature of SSS backscatter strength (BS) distribution. After that, a radiometric distortion correction model, incorporating the sediment BS information constraint, low-rank constraint on the incident illumination component, and an anisotropic total variation (ATV) constraint on the albedo, is presented. BS information is obtained through sediment classification based on mixed Gaussian model optimization. A minimization optimization method is used to solve the model, and an SSS image with corrected radiometric distortion is obtained. Experiments with different SSS images demonstrate the effectiveness of the proposed method.

An improved inversion method with additional constraints for surface mass load is developed for the sparse distribution of GNSS stations. Two synthetic mass load models from a checkerboard mass distribution and a more realistic distribution derived from GLDAS model were applied to test the method. We find that applying boundary constraints and the a priori reference model in regions with sparse sites significantly improves the inversion results by 88% and 60%, respectively. Synthetic tests demonstrate that the improved inversion method can identify the errors well and extract useful signal for inversion. Compared with previous method, the potential improvement of our method to mass inversion with a sparse distribution of sites is about 13.3% to 38.3%. The method was then applied to the Yunnan with real GNSS vertical motion for terrestrial water storage (TWS) inversion. The inverted results show good agreement with GLDAS and precipitation data, with a correlation coefficient of 0.85 and 0.61, respectively. Our spatiotemporal patterns resulted from GNSS manifest that the TWS in Yunnan shows a gradual decreasing slope distribution from the southwest mountains to the northeast plains, with an annual EWH amplitudes of 317mm during 2017-2019. Moreover, the GNSS inverted TWS show that Yunnan received abundant rainfall in 2017 and 2018, while experienced a severe drought event in 2019. All these results indicate that for GNSS network with sparse distribution over large areas, our improved inversion method with additional constraints can be a useful and reliable method for monitoring mass load change and identifying climate extremes.

Radiometric distortion caused by the time-varying gain (TVG), beam patterns, angular responses, and sonar altitude variations, highly degrades the quality of side-scan sonar (SSS) images. Thus, radiometric distortion correction becomes a fundamental step for SSS image processing which holds vital importance for geomorphic applications. However, existing methods cannot take the prior information of the acoustic illumination component as well as the feature of seafloor into consideration well, which would easily cause damage to the image and also always be powerless for residual stripe noise. In this paper, a novel radiometric correction method is proposed. First, we give a detailed analysis of the SSS imaging theory based on the Lambert’s law as well as the prior knowledge about the characteristics of SSS images. Then, incorporating the prior of the SSS imaging process, the low-rank constraint is specifically introduced for the illumination component, while the anisotropic total variation (ATV) constraint is used to constraint the albedo component, combining other constraints, a decomposition model is proposed to correct the radiometric distortion based on the SSS imaging theory. And an alternative minimization method has been adopted to solve the proposed model effectively. Experiments proved the validity of the proposed method.