Robust low-rank tensor completion via transformed tensor nuclear norm with total variation regularization

Qiu, Duo; Bai, Minru; Ng, Michael K.; Zhang, Xiongjun

doi:10.1016/j.neucom.2020.12.110

Cited by 47 publications

(31 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…L OW rank tensor recovery problem has gotten a lot of attention during the last decade. Furthermore, low rank tensor can be recovered efficiently using tensor (matrix) factorization [1], [2], [3], [4], [5], [6] and tensor rank minimization methods [7], [8], [9], [10], [11], [12], [13], [14], respectively. In this paper, we consider the tensor rank minimization problem.…”

Section: Introductionmentioning

confidence: 99%

Efficient Recovery of Low Rank Tensor via Triple Nonconvex Nonsmooth Rank Minimization

Yu¹

2022

Preprint

View full text Add to dashboard Cite

A tensor nuclear norm (TNN) based method for solving the tensor recovery problem was recently proposed, and it has achieved state-of-the-art performance. However, it may fail to produce a highly accurate solution since it tends to treats each frontal slice and each rank component of each frontal slice equally. In order to get a recovery with high accuracy, we propose a general and flexible rank relaxation function named double weighted nonconvex nonsmooth rank (DWNNR) relaxation function for efficiently solving the third order tensor recovery problem. The DWNNR relaxation function can be derived from the triple nonconvex nonsmooth rank (TNNR) relaxation function by setting the weight vector to be the hypergradient value of some concave function, thereby adaptively selecting the weight vector.To accelerate the proposed model, we develop the general inertial smoothing proximal gradient method. Furthermore, we prove that any limit point of the generated subsequence is a critical point. Combining the Kurdyka-Lojasiewicz (KL) property with some milder assumptions, we further give its global convergence guarantee. Experimental results on a practical tensor completion problem with both synthetic and real data, the results of which demonstrate the efficiency and superior performance of the proposed algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

Efficient Recovery of Low Rank Tensor via Triple Nonconvex Nonsmooth Rank Minimization

Yu¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The TT rank is defined as a vector formed by the rank of each unfolding-k matricization of the tensor. However, Tucker rank and TT rank may destroy the global correlation within the tensor due to their unfolding schemes [10,26].…”

mentioning

confidence: 99%

“…In particular, Song et al [31] proposed a novel unitary transform method and defined the transformed tensor nuclear norm (TTNN) and the transformed t-SVD. Compared the tubal rank based on the DFT, lower tubal rank can be obtained by using suitable unitary transformations [26,31]. Therefore, we mainly consider our model based on TTNN and also discuss the performance of our model with different transformations.…”

mentioning

confidence: 99%

“…On the other hand, total variation (TV) has attracted great attention in LRTC due to its superiority in edge preservation and noise removal, see [1,35,26,40] and the references therein. For instance, Yuan et al [40] considered both the noise intensity and the spatial property differences, and proposed the spectral-spatial adaptive hyperspectral TV (SSAHTV) method.…”

mentioning

confidence: 99%

“…By combining the TV and low-rank properties in both spectral and spatial modes, Wang et al [35] proposed the TV-regularized low-rank tensor decomposition (LRTDTV) model. Qiu et al [26] combined TTNN and TV regularization (TNTV) to recover tensors from partial observations and mixed noises. However, although TV regularization is popular in many applications, it also brings some undesired effects.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Enhancing low-rank tensor completion via first-order and second-order total variation regularizations

Gao

Huang

2023

JIMO

View full text Add to dashboard Cite

<p style='text-indent:20px;'>Recently, low-rank tensor completion (LRTC) has attracted significant attention since it has been applied in a wide variety of practical areas. Due to the edge-preserving and noise removal properties, total variation (TV) has been extensively used in LRTC problems. However, first-order TV usually causes unexpected staircase effects. In this paper, we focus on the LRTC problem with various degradations, which aims to recover third-order tensors from partial observations corrupted by sparse noise and Gaussian noise. We use the transformed tensor nuclear norm to explore global low-rankness, and the combination of first-order and second-order TV regularizations to alleviate the staircase effects caused by first-order TV. Based on these, we propose a first-order and second-order TV regularizations (FSTV) model. In order to solve the proposed FSTV model, a symmetric Gauss-Seidel based alternating direction method of multipliers is adopted. We also establish its global convergence under very mild conditions. Finally, extensive experiments on different video and multispectral image datasets show the superiority of the proposed method compared with several state-of-the-art methods.</p>

show abstract

Nonconvex optimization for third‐order tensor completion under wavelet transform

Bai

2023

Numerical Linear Algebra App

Self Cite

View full text Add to dashboard Cite

The main aim of this paper is to develop a nonconvex optimization model for third‐order tensor completion under wavelet transform. On the one hand, through wavelet transform of frontal slices, we divide a large tensor data into a main part tensor and three detail part tensors, and the elements of these four tensors are about a quarter of the original tensors. Solving these four small tensors can not only improve the operation efficiency, but also better restore the original tensor data. On the other hand, by using concave correction term, we are able to correct for low rank of tubal nuclear norm (TNN) data fidelity term and sparsity of ‐norm data fidelity term. We prove that the proposed algorithm can converge to some critical point. Experimental results on image, magnetic resonance imaging and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state‐of‐the‐arts including the TNN and other methods.

show abstract

Robust low-rank tensor completion via transformed tensor nuclear norm with total variation regularization

Cited by 47 publications

References 46 publications

Efficient Recovery of Low Rank Tensor via Triple Nonconvex Nonsmooth Rank Minimization

Efficient Recovery of Low Rank Tensor via Triple Nonconvex Nonsmooth Rank Minimization

Enhancing low-rank tensor completion via first-order and second-order total variation regularizations

Nonconvex optimization for third‐order tensor completion under wavelet transform

Contact Info

Product

Resources

About