106 research outputs found
Exact 3D seismic data reconstruction using Tubal-Alt-Min algorithm
Data missing is an common issue in seismic data, and many methods have been
proposed to solve it. In this paper, we present the low-tubal-rank tensor model
and a novel tensor completion algorithm to recover 3D seismic data. This is a
fast iterative algorithm, called Tubal-Alt-Min which completes our 3D seismic
data by exploiting the low-tubal-rank property expressed as the product of two
much smaller tensors. TubalAlt-Min alternates between estimating those two
tensor using least squares minimization. We evaluate its reconstruction
performance both on synthetic seismic data and land data survey. The
experimental results show that compared with the tensor nuclear norm
minimization algorithm, Tubal-Alt-Min improves the reconstruction error by
orders of magnitude
Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm
In this paper, we investigate tensor recovery problems within the tensor
singular value decomposition (t-SVD) framework. We propose the partial sum of
the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the
tensor tubal multi-rank. We build two PSTNN-based minimization models for two
typical tensor recovery problems, i.e., the tensor completion and the tensor
principal component analysis. We give two algorithms based on the alternating
direction method of multipliers (ADMM) to solve proposed PSTNN-based tensor
recovery models. Experimental results on the synthetic data and real-world data
reveal the superior of the proposed PSTNN
Tensor train rank minimization with nonlocal self-similarity for tensor completion
The tensor train (TT) rank has received increasing attention in tensor
completion due to its ability to capture the global correlation of high-order
tensors (). For third order visual data, direct TT rank
minimization has not exploited the potential of TT rank for high-order tensors.
The TT rank minimization accompany with \emph{ket augmentation}, which
transforms a lower-order tensor (e.g., visual data) into a higher-order tensor,
suffers from serious block-artifacts. To tackle this issue, we suggest the TT
rank minimization with nonlocal self-similarity for tensor completion by
simultaneously exploring the spatial, temporal/spectral, and nonlocal
redundancy in visual data. More precisely, the TT rank minimization is
performed on a formed higher-order tensor called group by stacking similar
cubes, which naturally and fully takes advantage of the ability of TT rank for
high-order tensors. Moreover, the perturbation analysis for the TT low-rankness
of each group is established. We develop the alternating direction method of
multipliers tailored for the specific structure to solve the proposed model.
Extensive experiments demonstrate that the proposed method is superior to
several existing state-of-the-art methods in terms of both qualitative and
quantitative measures
Novel Factorization Strategies for Higher Order Tensors: Implications for Compression and Recovery of Multi-linear Data
In this paper we propose novel methods for compression and recovery of
multilinear data under limited sampling. We exploit the recently proposed
tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic
framework for tensor decomposition. In contrast to popular existing tensor
decomposition techniques such as higher-order SVD (HOSVD), t-SVD has optimality
properties similar to the truncated SVD for matrices. Based on t-SVD, we first
construct novel tensor-rank like measures to characterize informational and
structural complexity of multilinear data. Following that we outline a
complexity penalized algorithm for tensor completion from missing entries. As
an application, 3-D and 4-D (color) video data compression and recovery are
considered. We show that videos with linear camera motion can be represented
more efficiently using t-SVD compared to traditional approaches based on
vectorizing or flattening of the tensors. Application of the proposed tensor
completion algorithm for video recovery from missing entries is shown to yield
a superior performance over existing methods. In conclusion we point out
several research directions and implications to online prediction of
multilinear data
Scaled Nuclear Norm Minimization for Low-Rank Tensor Completion
Minimizing the nuclear norm of a matrix has been shown to be very efficient
in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of
nuclear norms of matricizations of a tensor has been shown to be very efficient
in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to
recover a low-TT-rank sampled tensor by minimizing a weighted sum of nuclear
norms of unfoldings of the tensor. We provide numerical results to show that
our proposed method requires significantly less number of samples to recover to
the original tensor in comparison with simply minimizing the sum of nuclear
norms since the structure of the unfoldings in the TT tensor model is
fundamentally different from that of matricizations in the Tucker tensor model
Multidimensional Data Tensor Sensing for RF Tomographic Imaging
Radio-frequency (RF) tomographic imaging is a promising technique for
inferring multi-dimensional physical space by processing RF signals traversed
across a region of interest. However, conventional RF tomography schemes are
generally based on vector compressed sensing, which ignores the geometric
structures of the target spaces and leads to low recovery precision. The
recently proposed transform-based tensor model is more appropriate for sensory
data processing, as it helps exploit the geometric structures of the
three-dimensional target and improve the recovery precision. In this paper, we
propose a novel tensor sensing approach that achieves highly accurate
estimation for real-world three-dimensional spaces. First, we use the
transform-based tensor model to formulate a tensor sensing problem, and propose
a fast alternating minimization algorithm called Alt-Min. Secondly, we drive an
algorithm which is optimized to reduce memory and computation requirements.
Finally, we present evaluation of our Alt-Min approach using IKEA 3D data and
demonstrate significant improvement in recovery error and convergence speed
compared to prior tensor-based compressed sensing.Comment: 6 pages, 4 figure
Fast Randomized Algorithms for t-Product Based Tensor Operations and Decompositions with Applications to Imaging Data
Tensors of order three or higher have found applications in diverse fields,
including image and signal processing, data mining, biomedical engineering and
link analysis, to name a few. In many applications that involve for example
time series or other ordered data, the corresponding tensor has a
distinguishing orientation that exhibits a low tubal structure. This has
motivated the introduction of the tubal rank and the corresponding tubal
singular value decomposition in the literature. In this work, we develop
randomized algorithms for many common tensor operations, including tensor
low-rank approximation and decomposition, together with tensor multiplication.
The proposed tubal focused algorithms employ a small number of lateral and/or
horizontal slices of the underlying 3-rd order tensor, that come with {\em
relative error guarantees} for the quality of the obtained solutions. The
performance of the proposed algorithms is illustrated on diverse imaging
applications, including mass spectrometry data and image and video recovery
from incomplete and noisy data. The results show both good computational
speed-up vis-a-vis conventional completion algorithms and good accuracy.Comment: 31 pages, 6 figures, to appear in the SIAM Journal on Imaging
Science
Low-Rank Tensor Completion by Truncated Nuclear Norm Regularization
Currently, low-rank tensor completion has gained cumulative attention in
recovering incomplete visual data whose partial elements are missing. By taking
a color image or video as a three-dimensional (3D) tensor, previous studies
have suggested several definitions of tensor nuclear norm. However, they have
limitations and may not properly approximate the real rank of a tensor.
Besides, they do not explicitly use the low-rank property in optimization. It
is proved that the recently proposed truncated nuclear norm (TNN) can replace
the traditional nuclear norm, as a better estimation to the rank of a matrix.
Thus, this paper presents a new method called the tensor truncated nuclear norm
(T-TNN), which proposes a new definition of tensor nuclear norm and extends the
truncated nuclear norm from the matrix case to the tensor case. Beneficial from
the low rankness of TNN, our approach improves the efficacy of tensor
completion. We exploit the previously proposed tensor singular value
decomposition and the alternating direction method of multipliers in
optimization. Extensive experiments on real-world videos and images demonstrate
that the performance of our approach is superior to those of existing methods.Comment: Accepted as a poster presentation at the 24th International
Conference on Pattern Recognition in 20-24 August 2018, Beijing, Chin
A Tensor Completion Approach for Efficient and Robust Fingerprint-based Indoor Localization
The localization technology is important for the development of indoor
location-based services (LBS). The radio frequency (RF) fingerprint-based
localization is one of the most promising approaches. However, it is
challenging to apply this localization to real-world environments since it is
time-consuming and labor-intensive to construct a fingerprint database as a
prior for localization. Another challenge is that the presence of anomaly
readings in the fingerprints reduces the localization accuracy. To address
these two challenges, we propose an efficient and robust indoor localization
approach. First, we model the fingerprint database as a 3-D tensor, which
represents the relationships between fingerprints, locations and indices of
access points. Second, we introduce a tensor decomposition model for robust
fingerprint data recovery, which decomposes a partial observation tensor as the
superposition of a low-rank tensor and a spare anomaly tensor. Third, we
exploit the alternating direction method of multipliers (ADMM) to solve the
convex optimization problem of tensor-nuclear-norm completion for the anomaly
case. Finally, we verify the proposed approach on a ground truth data set
collected in an office building with size 80m times 20m. Experiment results
show that to achieve a same error rate 4%, the sampling rate of our approach is
only 10%, while it is 60% for the state-of-the-art approach. Moreover, the
proposed approach leads to a more accurate localization (nearly 20%, 0.6m
improvement) over the compared approach.Comment: 6 pages, 5 figure
Low Rank Tensor Completion for Multiway Visual Data
Tensor completion recovers missing entries of multiway data. Teh missing of
entries could often be caused during teh data acquisition and transformation.
In dis paper, we provide an overview of recent development in low rank tensor
completion for estimating teh missing components of visual data, e. g. , color
images and videos. First, we categorize these methods into two groups based on
teh different optimization models. One optimizes factors of tensor
decompositions wif predefined tensor rank. Teh other iteratively updates teh
estimated tensor via minimizing teh tensor rank. Besides, we summarize teh
corresponding algorithms to solve those optimization problems in details.
Numerical experiments are given to demonstrate teh performance comparison when
different methods are applied to color image and video processing
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