Underwater Image Enhancement with the Low-Rank Nonnegative Matrix Factorization Method

2021 ◽  
pp. 2154022
Author(s):  
Xiaopeng Liu ◽  
Cong Liu ◽  
Xiaochen Liu
Keyword(s):  
Image Enhancement ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Ground Truth ◽  
Factorization Method ◽  
Low Rank ◽  
Ground Truth Data ◽  
Underwater Image ◽  
Better Than

Due to the scattering and absorption effects in the undersea environment, underwater image enhancement is a challenging problem. To obtain the ground-truth data for training is also an open problem. So, the learning process is unavailable. In this paper, we propose a Low-Rank Nonnegative Matrix Factorization (LR-NMF) method, which only uses the degraded underwater image as input to generate the more clear and realistic image. According to the underwater image formation model, the degraded underwater image could be separated into three parts, the directed component, the back and forward scattering components. The latter two parts can be considered as scattering. The directed component is constrained to have a low rank. After that, the restored underwater image is obtained. The quantitative and qualitative analyses illustrate that the proposed method performed equivalent or better than the state-of-the-art methods. Yet, it’s simple to implement without the training process.

scholarly journals An Accelerated Symmetric Nonnegative Matrix Factorization Algorithm Using Extrapolation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1187
Author(s):  
Peitao Wang ◽  
Zhaoshui He ◽  
Jun Lu ◽  
Beihai Tan ◽  
YuLei Bai ◽  
...  
Keyword(s):  
Real World ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Tensor Factorization ◽  
Real World Data ◽  
Restart Strategy ◽  
Extrapolation Scheme ◽  
Symmetric Nonnegative Matrix Factorization

Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms.

A hybrid algorithm for low-rank approximation of nonnegative matrix factorization

2019 ◽  
Vol 364 ◽  
pp. 129-137
Author(s):  
Peitao Wang ◽  
Zhaoshui He ◽  
Kan Xie ◽  
Junbin Gao ◽  
Michael Antolovich ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Hybrid Algorithm ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation

scholarly journals Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zunyi Tang ◽  
Shuxue Ding ◽  
Zhenni Li ◽  
Linlin Jiang
Keyword(s):  
Sparse Representation ◽  
Dictionary Learning ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Coordinate Descent ◽  
Multispectral Data ◽  
Overcomplete Dictionary ◽  
Novel Method ◽  
Better Than

Sparse representation of signals via an overcomplete dictionary has recently received much attention as it has produced promising results in various applications. Since the nonnegativities of the signals and the dictionary are required in some applications, for example, multispectral data analysis, the conventional dictionary learning methods imposed simply with nonnegativity may become inapplicable. In this paper, we propose a novel method for learning a nonnegative, overcomplete dictionary for such a case. This is accomplished by posing the sparse representation of nonnegative signals as a problem of nonnegative matrix factorization (NMF) with a sparsity constraint. By employing the coordinate descent strategy for optimization and extending it to multivariable case for processing in parallel, we develop a so-called parallel coordinate descent dictionary learning (PCDDL) algorithm, which is structured by iteratively solving the two optimal problems, the learning process of the dictionary and the estimating process of the coefficients for constructing the signals. Numerical experiments demonstrate that the proposed algorithm performs better than the conventional nonnegative K-SVD (NN-KSVD) algorithm and several other algorithms for comparison. What is more, its computational consumption is remarkably lower than that of the compared algorithms.

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