Hyperspectral Image Restoration via Multi-mode and Double-weighted Tensor Nuclear Norm Minimization

Tensor nuclear norm (TNN) induced by tensor singular value decomposition plays an important role in hyperspectral image (HSI) restoration tasks. In this letter, we first consider three inconspicuous but crucial phenomenons in TNN. In the Fourier transform domain of HSIs, different frequency components contain different information; different singular values of each frequency component also represent different information. The two physical phenomenons lie not only in the spectral dimension but also in the spatial dimensions. Then, to improve the capability and flexibility of TNN for HSI restoration, we propose a multi-mode and double-weighted TNN based on the above three crucial phenomenons. It can adaptively shrink the frequency components and singular values according to their physical meanings in all modes of HSIs. In the framework of the alternating direction method of multipliers, we design an effective alternating iterative strategy to optimize our proposed model. Restoration experiments on both synthetic and real HSI datasets demonstrate their superiority against related methods

A General Destriping Framework for Remote Sensing Images Using Flatness Constraint

This paper proposes a general destriping framework using flatness constraints, where we can handle various regularization functions in a unified manner. Removing stripe noise, i.e., destriping, from remote sensing images is an essential task in terms of visual quality and subsequent processing. Most of the existing methods are designed by combining a particular image regularization with a stripe noise characterization that cooperates with the regularization, which precludes us to examine different regularizations to adapt to various target images. To resolve this, we formulate the destriping problem as a convex optimization problem involving a general form of image regularization and the flatness constraints, a newly introduced stripe noise characterization. This strong characterization enables us to consistently capture the nature of stripe noise, regardless of the choice of image regularization. For solving the optimization problem, we also develop an efficient algorithm based on a diagonally preconditioned primal-dual splitting algorithm (DP-PDS), which can automatically adjust the stepsizes. The effectiveness of our framework is demonstrated through destriping experiments, where we comprehensively compare combinations of image regularizations and stripe noise characterizations using hyperspectral images (HSI) and infrared (IR) videos.Comment: submitted to IEEE Transactions on Geoscience and Remote Sensin

Variable-Wise Diagonal Preconditioning for Primal-Dual Splitting: Design and Applications

This paper proposes a method of designing appropriate diagonal preconditioners for a preconditioned primal-dual splitting method (P-PDS). P-PDS can efficiently solve various types of convex optimization problems arising in signal processing and image processing. Since the appropriate diagonal preconditioners that accelerate the convergence of P-PDS vary greatly depending on the structure of the target optimization problem, a design method of diagonal preconditioners for PPDS has been proposed to determine them automatically from the problem structure. However, the existing method has two limitations: it requires direct access to all elements of the matrices representing the linear operators involved in the target optimization problem, and it is element-wise preconditioning, which makes certain types of proximity operators impossible to compute analytically. To overcome these limitations, we establish an Operator-norm-based design method of Variable-wise Diagonal Preconditioning (OVDP). First, the diagonal preconditioners constructed by OVDP are defined using only the operator norm or its upper bound of the linear operator thus eliminating the need for their explicit matrix representations. Furthermore, since our method is variable-wise preconditioning, it keeps all proximity operators efficiently computable. We also prove that our preconditioners satisfy the convergence conditions of PPDS. Finally, we demonstrate the effectiveness and utility of our method through applications to hyperspectral image mixed noise removal, hyperspectral unmixing, and graph signal recovery.Comment: Submitted to IEEE Transactions on Signal Processin

H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization

Recently, tensor singular value decomposition (t-SVD) has emerged as a promising tool for hyperspectral image (HSI) processing. In the t-SVD, there are two key building blocks: (i) the low-rank enhanced transform and (ii) the accompanying low-rank characterization of transformed frontal slices. Previous t-SVD methods mainly focus on the developments of (i), while neglecting the other important aspect, i.e., the exact characterization of transformed frontal slices. In this letter, we exploit the potentiality in both building blocks by leveraging the \underline{\bf H}ierarchical nonlinear transform and the \underline{\bf H}ierarchical matrix factorization to establish a new \underline{\bf T}ensor \underline{\bf F}actorization (termed as H2TF). Compared to shallow counter partners, e.g., low-rank matrix factorization or its convex surrogates, H2TF can better capture complex structures of transformed frontal slices due to its hierarchical modeling abilities. We then suggest the H2TF-based HSI denoising model and develop an alternating direction method of multipliers-based algorithm to address the resultant model. Extensive experiments validate the superiority of our method over state-of-the-art HSI denoising methods

Low-Rank Tensor Recovery with Euclidean-Norm-Induced Schatten-p Quasi-Norm Regularization

The nuclear norm and Schatten-$p$ quasi-norm of a matrix are popular rank proxies in low-rank matrix recovery. Unfortunately, computing the nuclear norm or Schatten-$p$ quasi-norm of a tensor is NP-hard, which is a pity for low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). In this paper, we propose a new class of rank regularizers based on the Euclidean norms of the CP component vectors of a tensor and show that these regularizers are monotonic transformations of tensor Schatten-$p$ quasi-norm. This connection enables us to minimize the Schatten-$p$ quasi-norm in LRTC and TRPCA implicitly. The methods do not use the singular value decomposition and hence scale to big tensors. Moreover, the methods are not sensitive to the choice of initial rank and provide an arbitrarily sharper rank proxy for low-rank tensor recovery compared to nuclear norm. We provide theoretical guarantees in terms of recovery error for LRTC and TRPCA, which show relatively smaller $p$ of Schatten-$p$ quasi-norm leads to tighter error bounds. Experiments using LRTC and TRPCA on synthetic data and natural images verify the effectiveness and superiority of our methods compared to baseline methods

Bayesian image restoration and bacteria detection in optical endomicroscopy

Optical microscopy systems can be used to obtain high-resolution microscopic images of tissue cultures and ex vivo tissue samples. This imaging technique can be translated for in vivo, in situ applications by using optical fibres and miniature optics. Fibred optical endomicroscopy (OEM) can enable optical biopsy in organs inaccessible by any other imaging systems, and hence can provide rapid and accurate diagnosis in a short time. The raw data the system produce is difficult to interpret as it is modulated by a fibre bundle pattern, producing what is called the “honeycomb effect”. Moreover, the data is further degraded due to the fibre core cross coupling problem. On the other hand, there is an unmet clinical need for automatic tools that can help the clinicians to detect fluorescently labelled bacteria in distal lung images. The aim of this thesis is to develop advanced image processing algorithms that can address the above mentioned problems. First, we provide a statistical model for the fibre core cross coupling problem and the sparse sampling by imaging fibre bundles (honeycomb artefact), which are formulated here as a restoration problem for the first time in the literature. We then introduce a non-linear interpolation method, based on Gaussian processes regression, in order to recover an interpretable scene from the deconvolved data. Second, we develop two bacteria detection algorithms, each of which provides different characteristics. The first approach considers joint formulation to the sparse coding and anomaly detection problems. The anomalies here are considered as candidate bacteria, which are annotated with the help of a trained clinician. Although this approach provides good detection performance and outperforms existing methods in the literature, the user has to carefully tune some crucial model parameters. Hence, we propose a more adaptive approach, for which a Bayesian framework is adopted. This approach not only outperforms the proposed supervised approach and existing methods in the literature but also provides computation time that competes with optimization-based methods