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IEEE JSTSP Article

Optimal rank selection is an important issue in tensor decomposition problems, especially for Tensor Train (TT) and Tensor Ring (TR) (also known as Tensor Chain) decompositions. In this paper, a new rank selection method for TR decomposition has been proposed for automatically finding near-optimal TR ranks, which result in a lower storage cost, especially for tensors with inexact TT or TR structures.

The emergence of big data and the multidimensional nature of wireless communication signals present significant opportunities for exploiting the versatility of tensor decompositions in associated data analysis and signal processing. The uniqueness of tensor decompositions, unlike matrix-based methods, can be guaranteed under very mild and natural conditions. 

The papers in this special section focus on tensor decomposition for signal processing and machine learning. Tensor decomposition, also called tensor factorization, is useful for representing and analyzing multi-dimensional data. Tensor decompositions have been applied in signal processing applications (speech, acoustics, communications, radar, biomedicine), machine learning (clustering, dimensionality reduction, latent factor models, subspace learning), and well beyond.

Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, which is often solved by minimizing a nonsmooth penalized co-log-likelihood function. Although the solution is easily interpretable with theoretic guarantees, its estimation relies on an optimization process that can take time. Considering the research effort in deep learning for image classification and segmentation, this class of methods offers a serious alternative to perform image restoration but stays challenging to solve inverse problems.

Image restoration is a critical component of image processing pipelines and for low-level computer vision tasks. Conventional image restoration approaches are mostly based on hand-crafted image priors. The inter-channel correlation of color images is not fully exploited. Motivated by the special characteristics of the inter-channel correlation (higher correlation for red/green and green/blue channels than for red/blue) in color images and general characteristics (green channel always shows the best image quality among the three color components) of distorted color images, in this paper, a three-stage convolutional neural network (CNN) structure is proposed for color image restoration tasks.

The papers in this special issue focus on deep learning for image/video restoration and compression. The huge success of deep-learning–based approaches in computer vision has inspired research in learned solutions to classic image/video processing problems, such as denoising, deblurring, dehazing, deraining, super-resolution (SR), and compression. Hence, learning-based methods have emerged as a promising nonlinear signal-processing framework for image/ video restoration and compression.

The papers in this special issue focus on deep learning for image/video restoration and compression. The huge success of deep-learning–based approaches in computer vision has inspired research in learned solutions to classic image/video processing problems, such as denoising, deblurring, dehazing, deraining, super-resolution (SR), and compression. Hence, learning-based methods have emerged as a promising nonlinear signal-processing framework for image/ video restoration and compression.

Dynamic range limitations in signal processing often lead to clipping, or saturation, in signals. The task of audio declipping is estimating the original audio signal, given its clipped measurements, and has attracted much interest in recent years. Audio declipping algorithms often make assumptions about the underlying signal, such as sparsity or low-rankness, and about the measurement system.

The papers from this special section focus on the restoration of udio content, in particular speech and music from degraded observations. This is a challenging and long-standing problem in audio processing. In particular this holds for severe degradations and incomplete observations, which are regularly encountered in practice. The papers in this section have been organized to gather contributions that would serve both as a comprehensive primer on the stateof- the-art, and a showcase of current developments within the field.

In magnetic resonance imaging (MRI), several images can be obtained using different imaging settings (e.g. T1, T2, DWI, and Flair). These images have similar anatomical structures but are with different contrasts, which provide a wealth of information for diagnosis.

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