29 research outputs found
Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition
Hyperspectral images (HSIs) are often corrupted by a mixture of several types
of noise during the acquisition process, e.g., Gaussian noise, impulse noise,
dead lines, stripes, and many others. Such complex noise could degrade the
quality of the acquired HSIs, limiting the precision of the subsequent
processing. In this paper, we present a novel tensor-based HSI restoration
approach by fully identifying the intrinsic structures of the clean HSI part
and the mixed noise part respectively. Specifically, for the clean HSI part, we
use tensor Tucker decomposition to describe the global correlation among all
bands, and an anisotropic spatial-spectral total variation (SSTV)
regularization to characterize the piecewise smooth structure in both spatial
and spectral domains. For the mixed noise part, we adopt the norm
regularization to detect the sparse noise, including stripes, impulse noise,
and dead pixels. Despite that TV regulariztion has the ability of removing
Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian
noise for some real-world scenarios. Then, we develop an efficient algorithm
for solving the resulting optimization problem by using the augmented Lagrange
multiplier (ALM) method. Finally, extensive experiments on simulated and
real-world noise HSIs are carried out to demonstrate the superiority of the
proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure
Constrained low-tubal-rank tensor recovery for hyperspectral images mixed noise removal by bilateral random projections
In this paper, we propose a novel low-tubal-rank tensor recovery model, which
directly constrains the tubal rank prior for effectively removing the mixed
Gaussian and sparse noise in hyperspectral images. The constraints of
tubal-rank and sparsity can govern the solution of the denoised tensor in the
recovery procedure. To solve the constrained low-tubal-rank model, we develop
an iterative algorithm based on bilateral random projections to efficiently
solve the proposed model. The advantage of random projections is that the
approximation of the low-tubal-rank tensor can be obtained quite accurately in
an inexpensive manner. Experimental examples for hyperspectral image denoising
are presented to demonstrate the effectiveness and efficiency of the proposed
method.Comment: Accepted by IGARSS 201
A Theoretically Guaranteed Quaternion Weighted Schatten p-norm Minimization Method for Color Image Restoration
Inspired by the fact that the matrix formulated by nonlocal similar patches
in a natural image is of low rank, the rank approximation issue have been
extensively investigated over the past decades, among which weighted nuclear
norm minimization (WNNM) and weighted Schatten -norm minimization (WSNM) are
two prevailing methods have shown great superiority in various image
restoration (IR) problems. Due to the physical characteristic of color images,
color image restoration (CIR) is often a much more difficult task than its
grayscale image counterpart. However, when applied to CIR, the traditional
WNNM/WSNM method only processes three color channels individually and fails to
consider their cross-channel correlations. Very recently, a quaternion-based
WNNM approach (QWNNM) has been developed to mitigate this issue, which is
capable of representing the color image as a whole in the quaternion domain and
preserving the inherent correlation among the three color channels. Despite its
empirical success, unfortunately, the convergence behavior of QWNNM has not
been strictly studied yet. In this paper, on the one side, we extend the WSNM
into quaternion domain and correspondingly propose a novel quaternion-based
WSNM model (QWSNM) for tackling the CIR problems. Extensive experiments on two
representative CIR tasks, including color image denoising and deblurring,
demonstrate that the proposed QWSNM method performs favorably against many
state-of-the-art alternatives, in both quantitative and qualitative
evaluations. On the other side, more importantly, we preliminarily provide a
theoretical convergence analysis, that is, by modifying the quaternion
alternating direction method of multipliers (QADMM) through a simple
continuation strategy, we theoretically prove that both the solution sequences
generated by the QWNNM and QWSNM have fixed-point convergence guarantees.Comment: 46 pages, 10 figures; references adde
Robust subspace clustering via joint weighted Schatten-p norm and Lq norm minimization
© 2017 SPIE. Low-rank representation (LRR) has been successfully applied to subspace clustering. However, the nuclear norm in the standard LRR is not optimal for approximating the rank function in many real-world applications. Meanwhile, the L21 norm in LRR also fails to characterize various noises properly. To address the above issues, we propose an improved LRR method, which achieves low rank property via the new formulation with weighted Schatten-p norm and Lq norm (WSPQ). Specifically, the nuclear norm is generalized to be the Schatten-p norm and different weights are assigned to the singular values, and thus it can approximate the rank function more accurately. In addition, Lq norm is further incorporated into WSPQ to model different noises and improve the robustness. An efficient algorithm based on the inexact augmented Lagrange multiplier method is designed for the formulated problem. Extensive experiments on face clustering and motion segmentation clearly demonstrate the superiority of the proposed WSPQ over several state-of-the-art methods
Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing
Hyperspectral imaging, also known as image spectrometry, is a landmark
technique in geoscience and remote sensing (RS). In the past decade, enormous
efforts have been made to process and analyze these hyperspectral (HS) products
mainly by means of seasoned experts. However, with the ever-growing volume of
data, the bulk of costs in manpower and material resources poses new challenges
on reducing the burden of manual labor and improving efficiency. For this
reason, it is, therefore, urgent to develop more intelligent and automatic
approaches for various HS RS applications. Machine learning (ML) tools with
convex optimization have successfully undertaken the tasks of numerous
artificial intelligence (AI)-related applications. However, their ability in
handling complex practical problems remains limited, particularly for HS data,
due to the effects of various spectral variabilities in the process of HS
imaging and the complexity and redundancy of higher dimensional HS signals.
Compared to the convex models, non-convex modeling, which is capable of
characterizing more complex real scenes and providing the model
interpretability technically and theoretically, has been proven to be a
feasible solution to reduce the gap between challenging HS vision tasks and
currently advanced intelligent data processing models