95 research outputs found
Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration
Hyperspectral imaging, providing abundant spatial and spectral information
simultaneously, has attracted a lot of interest in recent years. Unfortunately,
due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to
various degradations, such noises (random noise, HSI denoising), blurs
(Gaussian and uniform blur, HSI deblurring), and down-sampled (both spectral
and spatial downsample, HSI super-resolution). Previous HSI restoration methods
are designed for one specific task only. Besides, most of them start from the
1-D vector or 2-D matrix models and cannot fully exploit the structurally
spectral-spatial correlation in 3-D HSI. To overcome these limitations, in this
work, we propose a unified low-rank tensor recovery model for comprehensive HSI
restoration tasks, in which non-local similarity between spectral-spatial cubic
and spectral correlation are simultaneously captured by 3-order tensors.
Further, to improve the capability and flexibility, we formulate it as a
weighted low-rank tensor recovery (WLRTR) model by treating the singular values
differently, and study its analytical solution. We also consider the exclusive
stripe noise in HSI as the gross error by extending WLRTR to robust principal
component analysis (WLRTR-RPCA). Extensive experiments demonstrate the proposed
WLRTR models consistently outperform state-of-the-arts in typical low level
vision HSI tasks, including denoising, destriping, deblurring and
super-resolution.Comment: 22 pages, 22 figure
A General Model for Robust Tensor Factorization with Unknown Noise
Because of the limitations of matrix factorization, such as losing spatial
structure information, the concept of low-rank tensor factorization (LRTF) has
been applied for the recovery of a low dimensional subspace from high
dimensional visual data. The low-rank tensor recovery is generally achieved by
minimizing the loss function between the observed data and the factorization
representation. The loss function is designed in various forms under different
noise distribution assumptions, like norm for Laplacian distribution and
norm for Gaussian distribution. However, they often fail to tackle the
real data which are corrupted by the noise with unknown distribution. In this
paper, we propose a generalized weighted low-rank tensor factorization method
(GWLRTF) integrated with the idea of noise modelling. This procedure treats the
target data as high-order tensor directly and models the noise by a Mixture of
Gaussians, which is called MoG GWLRTF. The parameters in the model are
estimated under the EM framework and through a new developed algorithm of
weighted low-rank tensor factorization. We provide two versions of the
algorithm with different tensor factorization operations, i.e., CP
factorization and Tucker factorization. Extensive experiments indicate the
respective advantages of this two versions in different applications and also
demonstrate the effectiveness of MoG GWLRTF compared with other competing
methods.Comment: 13 pages, 8 figure
Color Image and Multispectral Image Denoising Using Block Diagonal Representation
Filtering images of more than one channel is challenging in terms of both
efficiency and effectiveness. By grouping similar patches to utilize the
self-similarity and sparse linear approximation of natural images, recent
nonlocal and transform-domain methods have been widely used in color and
multispectral image (MSI) denoising. Many related methods focus on the modeling
of group level correlation to enhance sparsity, which often resorts to a
recursive strategy with a large number of similar patches. The importance of
the patch level representation is understated. In this paper, we mainly
investigate the influence and potential of representation at patch level by
considering a general formulation with block diagonal matrix. We further show
that by training a proper global patch basis, along with a local principal
component analysis transform in the grouping dimension, a simple
transform-threshold-inverse method could produce very competitive results. Fast
implementation is also developed to reduce computational complexity. Extensive
experiments on both simulated and real datasets demonstrate its robustness,
effectiveness and efficiency
Denoising and Completion of 3D Data via Multidimensional Dictionary Learning
In this paper a new dictionary learning algorithm for multidimensional data
is proposed. Unlike most conventional dictionary learning methods which are
derived for dealing with vectors or matrices, our algorithm, named KTSVD,
learns a multidimensional dictionary directly via a novel algebraic approach
for tensor factorization as proposed in [3, 12, 13]. Using this approach one
can define a tensor-SVD and we propose to extend K-SVD algorithm used for 1-D
data to a K-TSVD algorithm for handling 2-D and 3-D data. Our algorithm, based
on the idea of sparse coding (using group-sparsity over multidimensional
coefficient vectors), alternates between estimating a compact representation
and dictionary learning. We analyze our KTSVD algorithm and demonstrate its
result on video completion and multispectral image denoising.Comment: 9 pages, submitted to Conference on Computer Vision and Pattern
Recognition (CVPR) 201
Efficient Two-Dimensional Sparse Coding Using Tensor-Linear Combination
Sparse coding (SC) is an automatic feature extraction and selection technique
that is widely used in unsupervised learning. However, conventional SC
vectorizes the input images, which breaks apart the local proximity of pixels
and destructs the elementary object structures of images. In this paper, we
propose a novel two-dimensional sparse coding (2DSC) scheme that represents the
input images as the tensor-linear combinations under a novel algebraic
framework. 2DSC learns much more concise dictionaries because it uses the
circular convolution operator, since the shifted versions of atoms learned by
conventional SC are treated as the same ones. We apply 2DSC to natural images
and demonstrate that 2DSC returns meaningful dictionaries for large patches.
Moreover, for mutli-spectral images denoising, the proposed 2DSC reduces
computational costs with competitive performance in comparison with the
state-of-the-art algorithms
SMDS-Net: Model Guided Spectral-Spatial Network for Hyperspectral Image Denoising
Deep learning (DL) based hyperspectral images (HSIs) denoising approaches
directly learn the nonlinear mapping between observed noisy images and
underlying clean images. They normally do not consider the physical
characteristics of HSIs, therefore making them lack of interpretability that is
key to understand their denoising mechanism.. In order to tackle this problem,
we introduce a novel model guided interpretable network for HSI denoising.
Specifically, fully considering the spatial redundancy, spectral low-rankness
and spectral-spatial properties of HSIs, we first establish a subspace based
multi-dimensional sparse model. This model first projects the observed HSIs
into a low-dimensional orthogonal subspace, and then represents the projected
image with a multidimensional dictionary. After that, the model is unfolded
into an end-to-end network named SMDS-Net whose fundamental modules are
seamlessly connected with the denoising procedure and optimization of the
model. This makes SMDS-Net convey clear physical meanings, i.e., learning the
low-rankness and sparsity of HSIs. Finally, all key variables including
dictionaries and thresholding parameters are obtained by the end-to-end
training. Extensive experiments and comprehensive analysis confirm the
denoising ability and interpretability of our method against the
state-of-the-art HSI denoising methods.Comment: The experimental settings have been update
A Low-rank Tensor Dictionary Learning Method for Multi-spectral Images Denoising
As a 3-order tensor, a multi-spectral image (MSI) has dozens of spectral
bands, which can deliver more information for real scenes. However, real MSIs
are often corrupted by noises in the sensing process, which will further
deteriorate the performance of higher-level classification and recognition
tasks. In this paper, we propose a Low-rank Tensor Dictionary Learning (LTDL)
method for MSI denoising. Firstly, we extract blocks from the MSI and cluster
them into groups. Then instead of using the exactly low-rank model, we consider
a nearly low-rank approximation, which is closer to the latent low-rank
structure of the clean groups of real MSIs. In addition, we propose to learn an
spatial dictionary and an spectral dictionary, which contain the spatial
features and spectral features respectively of the whole MSI and are shared
among different groups. Hence the LTDL method utilizes both the latent low-rank
prior of each group and the correlation of different groups via the shared
dictionaries. Experiments on synthetic data validate the effectiveness of
dictionary learning by the LTDL. Experiments on real MSIs demonstrate the
superior denoising performance of the proposed method in comparison to
state-of-the-art methods
Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising
Non-local low-rank tensor approximation has been developed as a
state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately,
with more spectral bands for HSI, while the running time of these methods
significantly increases, their denoising performance benefits little. In this
paper, we claim that the HSI underlines a global spectral low-rank subspace,
and the spectral subspaces of each full band patch groups should underlie this
global low-rank subspace. This motivates us to propose a unified
spatial-spectral paradigm for HSI denoising. As the new model is hard to
optimize, we further propose an efficient algorithm for optimization, which is
motivated by alternating minimization. This is done by first learning a
low-dimensional projection and the related reduced image from the noisy HSI.
Then, the non-local low-rank denoising and iterative regularization are
developed to refine the reduced image and projection, respectively. Finally,
experiments on synthetic and both real datasets demonstrate the superiority
against the other state-of-the-arts HSI denoising methods
Blind Multi-spectral Image Decomposition by 3D Nonnegative Tensor Factorization
Alpha-divergence based nonnegative tensor factorization (NTF) is applied to blind multi-spectral image (MSI) decomposition. Matrix of spectral profiles and matrix of spatial distributions of the materials resident in the image are identified from the factors in Tucker3 and PARAFAC models. NTF preserves local structure in the MSI that is lost, due to vectorization of the image, with nonnegative matrix factorization (NMF)- or independent component analysis (ICA)-based decompositions. Moreover, NTF based on PARAFAC model is unique up to permutation and scale under mild conditions. To achieve this, NMF- and ICA-based factorizations respectively require enforcement of sparseness (orthogonality) and statistical independence constraints on the spatial distributions of the materials resident in the MSI, and that is not true. We demonstrate efficiency of the NTF-based factorization in relation to NMF- and ICA-based factorizations on blind decomposition of the experimental MSI with the known ground truth
Tensor Low Rank Modeling and Its Applications in Signal Processing
Modeling of multidimensional signal using tensor is more convincing than
representing it as a collection of matrices. The tensor based approaches can
explore the abundant spatial and temporal structures of the mutlidimensional
signal. The backbone of this modeling is the mathematical foundations of tensor
algebra. The linear transform based tensor algebra furnishes low complex and
high performance algebraic structures suitable for the introspection of the
multidimensional signal. A comprehensive introduction of the linear transform
based tensor algebra is provided from the signal processing viewpoint. The rank
of a multidimensional signal is a precious property which gives an insight into
the structural aspects of it. All natural multidimensional signals can be
approximated to a low rank signal without losing significant information. The
low rank approximation is beneficial in many signal processing applications
such as denoising, missing sample estimation, resolution enhancement,
classification, background estimation, object detection, deweathering,
clustering and much more applications. Detailed case study of the ways and
means of the low rank modeling in the above said signal processing applications
are also presented
- …