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Model-based hyperspectral image (HSI) denoising methods have attracted continuous attention in the past decades, due to their effectiveness and interpretability. In this work, we aim at advancing model-based HSI denoising, through sophisticated investigation for both the fidelity and regularization terms, or correspondingly noise and prior, by virtue of several recently developed techniques. Specifically, we formulate a novel unified probabilistic model for the HSI denoising task, within which the noise is assumed as pixel-wise non-independent and identically distributed (non-i.i.d) Gaussian predicted by a pre-trained neural network, and the prior for the HSI image is designed by incorporating the deep image prior (DIP) with total variation (TV) and spatio-spectral TV. To solve the resulted maximum a posteriori (MAP) estimation problem, we design a Monte Carlo Expectation–Maximization (MCEM) algorithm, in which the stochastic gradient Langevin dynamics (SGLD) method is used for computing the E-step, and the alternative direction method of multipliers (ADMM) is adopted for solving the optimization in the M-step. Experiments on both synthetic and real noisy HSI datasets have been conducted to verify the effectiveness of the proposed method.

Time–frequency analysis is an important tool used for the processing and interpretation of non-stationary signals, such as seismic data and remote sensing data. In this paper, based on the novel short-time fractional Fourier transform (STFRFT), a new modified STFRFT is first proposed which can also generalize the properties of the modified short-time Fourier transform (STFT). Then, in the modified STFRFT domain, we derive the instantaneous frequency estimator for the chirp signal and present a new type of synchrosqueezing STFRFT (FRSST). The proposed FRSST presents many results similar to those of the synchrosqueezing STFT (FSST), and it extends the harmonic signal to a chirp signal that offers attractive new features. Furthermore, we provide a detailed analysis of the signal reconstruction, theories, and some properties of the proposed FRSST. Several experiments are conducted, and all of the results illustrate that the proposed FRSST is more effective than the FSST. Finally, based on the linear amplitude modulation and frequency modulation signal, we present a derivation for analyzing the limitations of the FRSST.

The rapid development of big data breeds data science. Understanding and mastering the internal pattern of the value generation of big data is important for improving digitization and the covergence of data science with management science, computer science, and other disciplines. In this study, we discuss the significance of data science for the development of science and technology and social progress. Based on the interpretation of the connotation of data science, we introduce the definition of data science and review its formation by summarizing the major progress of related disciplines. We also discuss the research methodologies, development patterns and trends, and technical directions of data science. Finally, we make suggestions for data science to promote the development of data-based science and technology.

In hyperspectral image (HSI) processing, a fundamental issue is to restore HSI data from various degradations such as noise corruption and information missing. However, most existing methods more or less ignore the abundant prior knowledge on HSIs and the embedded noise, leading to suboptimal performance in practice. In this article, we propose a novel HSI restoration method by fully considering the intrinsic image structures and the complex noise characteristics. For HSIs, the global correlation is captured by the Kronecker-basis-representation-based tensor low-rankness measure, which integrates the insights delivered by both CP and Tucker decompositions; the local regularity is depicted by a plug-and-play spatial-spectral convolutional neural network with strong fitting ability to complex image features. For realistic noise, its statistical characteristics are encoded by a nonidentical and nonindependent distributed mixture of Gaussians distribution with flexible fitting capability. Then, we incorporate these image and noise priors into a probabilistic model based on the maximum a posteriori principle, and develop a solving scheme by combining expectation-maximization and alternating direction method of multipliers. Extensive experimental results on both simulated and real scenarios demonstrate the effectiveness of the proposed method and its superiority over the compared state-of-the- arts.

Noise removal is a fundamental problem in remote sensing image processing. Most existing methods, however, have not yet attained sufficient robustness in practice, due to more or less neglecting the intrinsic structures of remote sensing images and/or underestimating the complexity of realistic noise. In this paper, we propose a new remote sensing image denoising method by integrating intrinsic image characterization and robust noise modeling. Specifically, we use low-Tucker-rank tensor approximation to capture the global multi-factor correlation within the underlying image, and adopt a non-identical and non-independent distributed mixture of Gaussians (non-i.i.d. MoG) assumption to encode the statistical configurations of the embedded noise. Then, we incorporate the proposed image and noise priors into a full Bayesian generative model and design an efficient variational Bayesian algorithm to infer all involved variables by closed-form equations. Moreover, adaptive strategies for the selection of hyperparameters are further developed to make our algorithm free from burdensome hyperparameter-tuning. Extensive experiments on both simulated and real multispectral/hyperspectral images demonstrate the superiority of the proposed method over the compared state-of-the-art ones.

In this paper, a new supervised classification algorithm which simultaneously considers spectral and spatial information of a hyperspectral image (HSI) is proposed. Since HSI always contains complex noise (such as mixture of Gaussian and sparse noise), the quality of the extracted feature inclines to be decreased. To tackle this issue, we utilize the low-rank property of local three-dimensional, patch and adopt complex noise strategy to model the noise embedded in each local patch. Specifically, we firstly use the mixture of Gaussian (MoG) based low-rank matrix factorization (LRMF) method to simultaneously extract the feature and remove noise from each local matrix unfolded from the local patch. Then, a classification map is obtained by applying some classifier to the extracted low-rank feature. Finally, the classification map is processed by Markov random field (MRF) in order to further utilize the smoothness property of the labels. To ease experimental comparison for different HSI classification methods, we built an open package to make the comparison fairly and efficiently. By using this package, the proposed classification method is verified to obtain better performance compared with other state-of-the-art methods.

This note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frame D. By introducing the notion of block D-restricted isometry property (D-RIP), we establish several sufficient conditions for the proposed mixed l2/l1-analysis method to guarantee stable recovery of nearly block-sparse signals in terms of D. One of the main results of this note shows that if the measurement matrix satisfies the block D-RIP with constants δk

Within the conventional framework of a native space structure, a smooth kernel generates a small native space, and radial basis functions stemming from the smooth kernel are intended to approximate only functions from this small native space. In this paper, we embed the smooth radial basis functions in a larger native space generated by a less smooth kernel and use them to interpolate the samples. Our result shows that there exists a linear combination of spherical radial basis functions that can both exactly interpolate samples generated by functions in the larger native space and near best approximate the target function.

We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency estimation in the framework of atomic norm minimization (ANM), we introduce multiple positive-semidenite block matrices composed of Hankel and Toeplitz submatrices and formulate the ANM problem as a convex structured low-rank approximation (SLRA) problem. The proposed SLRA is a semidenite programming and has substantial differences from existing such formulations without using the CA property. The proposed approach is termed as SLRA-based ANM for CA frequency estimation (SACA). We provide theoretical guarantees and extensive simulations that validate the advantages of SACA. [ABSTRACT FROM AUTHOR]