Improved non-negative tensor Tucker decomposition algorithm for interference hyper-spectral image compression

International audience

On the uniqueness of the positive Z-eigenvector for nonnegative tensors

We study the real and complex geometric simplicity of nonnegative irreducible tensors. First, we prove some basic conclusions. Based on the conclusions, the real geometric simplicity of the spectral radius of an evenorder nonnegative irreducible tensor is proved. For an odd-order nonnegative irreducible tensor, sufficient conditions are investigated to ensure the spectral radius to be real geometrically simple. Furthermore, the complex geometric simplicity of nonnegative irreducible tensors is also studied.

The main purpose of this paper is to consider the Perron pair of an irreducible and symmetric nonnegative tensor and the smallest eigenvalue of an irreducible and symmetric nonsingular \(\mathscr {M}\)-tensor. We analyze the analytical property of an algebraic simple eigenvalue of symmetric tensors. We also derive an inequality about the Perron pair of nonnegative tensors based on plane stochastic tensors. We finally consider the perturbation of the smallest eigenvalue of nonsingular \(\mathscr {M}\)-tensors and design a strategy to compute its smallest eigenvalue. We verify our results via random numerical examples.

Due to the imaging mechanism of Synthetic Aperture Radars (SARs), the target shape on an SAR image is sensitive to the radar incidence angle and target azimuth, but there is strong correlation and redundancy between adjacent azimuth images of SAR targets. This paper studies multi-angle SAR image reconstruction based on non-negative Tucker decomposition using adjacent azimuth images reconstructed to form a sparse tensor. Sparse tensors are used to perform non-negative Tucker decomposition, resulting in non-negative core tensors and factor matrices. The reconstruction tensor is obtained by calculating the n-mode product of the core tensor and the factor matrix, and then image reconstruction is realized. The similarity between the original image and the reconstructed image is calculated by using the structural similarity index and the cosine of the angle between the feature vectors. The reconstruction results of three target images of MSTAR show that the reconstructed image has a similarity higher than 95% with the original image in most cases, which can support target recognition under sparse observation to a certain extent.

In this paper, we present an algorithm that allows us to compute the permanent of a tensor by using Laplace expansion. We prove that the permanent of a $4$-dimensional polystochastic $(0,1)$-tensor of order $n$ constructed using a special $n\times (n-1)$ row-Latin rectangle $R$ with no transversals is positive. Also, we show that the permanent of an even-dimensional polystochastic $(0,1)$-tensor of order $n$ constructed using the row-Latin rectangle $R$ is positive. The result obtained here proves that each odd-dimensional Latin hypercube of order $4$ has a transversal (Wanless' conjecture for odd-dimensional Latin hypercubes of order $4$). We prove that the number of perfect matchings of the bipartite hypergraph associated to an even-dimensional polystochastic $(0,1)$-tensor of order $4$ is positive. Furthermore, we extend some results concerning polystochastic $(0,1)$-tensors to nonnegative polystochastic tensors. Moreover, we prove that the permanent of a $ 4 $-dimensional nonnegative polystochastic tensor of order $n$ constructed using the row-Latin rectangle $R$ is positive. More generally, we show that the permanent of an even-dimensional nonnegative polystochastic tensor of order $n$ constructed using the row-Latin rectangle $R$ is positive. The result obtained here proves that the permanent of an even-dimensional nonnegative polystochastic tensor of order $4$ is positive.

The data size of hyperspectral image is too large for storage and transmission, and it has become a bottleneck restricting its applications. So it is necessary to study a high efficiency compression method for hyperspectral image. Prediction encoding is easy to realize and has been studied widely in the hyperspectral image compression field. Fractal coding has the advantages of high compression ratio, resolution independence, and a fast decoding speed, but its application in the hyperspectral image compression field is not popular. In this paper, we propose a novel algorithm for hyperspectral image compression based on hybrid prediction and fractal. Intraband prediction is implemented to the first band and all the remaining bands are encoded by modified fractal coding algorithm. The proposed algorithm can effectively exploit the spectral correlation in hyperspectral image, since each range block is approximated by the domain block in the adjacent band, which is of the same size as the range block. Experimental results indicate that the proposed algorithm provides very promising performance at low bitrate. Compared to other algorithms, the encoding complexity is lower, the decoding quality has a great enhancement, and the PSNR can be increased by about 5 dB to 10 dB.

Objectives. The widespread use of systems for capturing light fields is due to the high quality of the reproduced image. This type of capture, although qualitatively superior to traditional methods to capturing volumetric images, generates a huge amount of data needed to reconstruct the original captured 4D light field. The purpose of the work is to consider traditional and extended to four-dimensional image compression algorithms, to perform a comparative analysis and determine the most suitable.Methods. Mathematical methods of signal processing and methods of statistical analysis are used.Results. Algorithms are compared and analyzed in relation to the compression of four-dimensional light fields using the PSNR metric. The selected evaluation criterion is affected not only by the dimension of the compression algorithm, but also by the distance of the baseline of the capture setting, since the difference between images increases with the distance between the optical centers of each camera matrix. Thus, for installations consisting of an array of machine vision cameras located on racks and placed in a room, the obvious choice would be to use conventional image compression methods. Furthermore, based on the assessment of the arbitrariness of video compression methods, it should be noted that the XVC algorithm remains undervalued, although its results are higher. Algorithm AV1 can be considered the next in order of importance. It has been established that the latest compression algorithms show higher performance if compared to their predecessors. It has also been shown that with a small distance between the optical centers of the captured images, the use of video compression algorithms is preferable to the use of image compression algorithms, since they show better results in both three-dimensional and four-dimensional versions.Conclusions. A comparison of the results obtained shows the need to use algorithms from the video compression family (XVC, AV1) on installations with a long baseline (mounted on camera stands). When working with integrated light field cameras (Lytro) and setting the capture with a short baseline, it is recommended to use image compression algorithms (JPEG). In general, video compression algorithms are recommended, in particular XVC, since on average it shows an acceptable level of PSNR in both the case of a short and long installation baseline.

In this paper, we propose an efficient compression algorithm for hyperspectral images. It is based on the correlation coefficients adaptive AT-3DSPIHT coding in the domain of WPT (wavelet packet transform). According to the characteristics of correlation coefficients between spectral bands, a binary tree spectral band grouping algorithm is carried out to divide the adjacent spectral bands into different mode groups. Along with this, WPT with the corresponding decomposition levels and a proper AT-3D zerotree are determined adaptively. Several AVIRIS images are used to evaluate the proposed algorithm. Compared with the existing 3D-based algorithms, the proposed adaptive AT-3DSPIHT achieves the best compression performance at lower rates. Moreover, at the low correlated adjacent bands, our proposed algorithm also beats the 2DSPIHT and JPEG2000-MC algorithm respectively.

DSC的超光谱图像无损压缩算法

Multiplicative update algorithms are important tools for information retrieval, image processing, and pattern recognition. However, when the graph regularization is added to the cost function, different classes of sample data may be mapped to the same subspace, which leads to the increase of data clustering error rate. In this paper, an improved nonnegative matrix factorization (NMF) cost function is introduced. Based on the cost function, a class of novel graph regularized NMF algorithms is developed, which results in a class of extended multiplicative update algorithms with manifold structure regularization. Analysis shows that in the learning, the proposed algorithms can efficiently minimize the rank of the data representation matrix. Theoretical results presented in this paper are confirmed by simulations. For different initializations and data sets, variation curves of cost functions and decomposition data are presented to show the convergence features of the proposed update rules. Basis images, reconstructed images, and clustering results are utilized to present the efficiency of the new algorithms. Last, the clustering accuracies of different algorithms are also investigated, which shows that the proposed algorithms can achieve state-of-the-art performance in applications of image clustering.

The Gaussian and Gaussian-sigmoidal primaries are introduced as initialization functions in the nonnegative matrix factorization (NNMF) method to achieve more consistent error statistics. The proposed NNMF method with multiplicative update algorithm is employed for reconstruction of spectral data of Munsell and Colorchecker DC datasets from the corresponding CIEXYZ tristimulus values and the resultant achievements are compared with those obtained from PCA and the classical NNMF techniques. Both colorimetric and spectrophotometric errors between the original and the reconstructed spectra are used for the evaluation of reconstruction methods. While run to run variability of the classical NNMF method with multiplicative update algorithm is significantly remarkable, the stability of the suggested technique is fairly high, similar to the PCA method. The ensuing findings show that the embedding of Gaussian initializing vectors in NNMF method provide the all positive bases that enhance both the accuracy of Gaussian method and the reliability of NNMF technique.

Graphics Processing Units (GPU) are becoming a widespread tool for general-purpose scientific computing, and are attracting interest for future onboard satellite image processing payloads due to their ability to perform massively parallel computations. This paper describes the GPU implementation of an algorithm for onboard lossy hyperspectral image compression, and proposes an architecture that allows to accelerate the compression task by parallelizing it on the GPU. The selected algorithm was amenable to parallel computation owing to its block-based operation, and has been optimized here to facilitate GPU implementation incurring a negligible overhead with respect to the original single-threaded version. In particular, a parallelization strategy has been designed for both the compressor and the corresponding decompressor, which are implemented on a GPU using Nvidia's CUDA parallel architecture. Experimental results on several hyperspectral images with different spatial and spectral dimensions are presented, showing significant speed-ups with respect to a single-threaded CPU implementation. These results highlight the significant benefits of GPUs for onboard image processing, and particularly image compression, demonstrating the potential of GPUs as a future hardware platform for very high data rate instruments.

The main aim of this paper is to develop a new algorithm for computing a nonnegative low multi‐rank tensor approximation for a nonnegative tensor. In the literature, there are several nonnegative tensor factorizations or decompositions, and their approaches are to enforce the nonnegativity constraints in the factors of tensor factorizations or decompositions. In this paper, we study nonnegativity constraints in tensor entries directly, and a low rank approximation for the transformed tensor by using discrete Fourier transformation matrix, discrete cosine transformation matrix, or unitary transformation matrix. This strategy is particularly useful in imaging science as nonnegative pixels appear in tensor entries and a low rank structure can be obtained in the transformation domain. We propose an alternating projections algorithm for computing such a nonnegative low multi‐rank tensor approximation. The convergence of the proposed projection method is established. Numerical examples for multidimensional images are presented to demonstrate that the performance of the proposed method is better than that of nonnegative low Tucker rank tensor approximation and the other nonnegative tensor factorizations and decompositions.

Reverberant signal separation using optimized complex sparse nonnegative tensor deconvolution on spectral covariance matrix