﻿ 基于字典算法的OCT图像散斑稀疏降噪
 光电工程  2019, Vol. 46 Issue (6): 1      DOI: 10.12086/oee.2019.180572

OCT image speckle sparse noise reduction based on dictionary algorithm
Wang Fan, Chen Minghui, Gao Naijun, Zhang Chenxi, Zheng Gang
Institute of Biomedical Optics and Optometry, Shanghai Institute for Minimally Invasive Therapy, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: As a new non-invasive and high-resolution scanning method, optical coherence tomography (OCT) has been widely used in clinical practice, but OCT images have serious speckle noise, which greatly affects the diagnosis of diseases. Two original dictionary noise reduction algorithms have been improved for multiplicative speckle noise in OCT. The algorithm first performs logarithmic transformation on OCT images, uses orthogonal matching pursuit algorithm for sparse coding, and K singular value decomposition learning algorithm to update adaptive dictionary. Finally, it returns to the space domain through weighted average and exponential transformation. The experimental results show that the improved two dictionary algorithms can effectively reduce the speckle noise in OCT images and obtain good visual effects. The noise reduction effect is evaluated by four factors: mean squared error (MSE), peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and edge-preserving index (EPI). Compared with the two original dictionary noise reduction algorithms and the traditional filtering algorithms, the noise reduction effect of the two improved dictionary algorithms is better than that of other algorithms, and the improved adaptive dictionary algorithm performs better.
Keywords: optical coherence tomography    sparse representation    dictionary learning    speckle    image noise reduction

1 引言

2 方法

2.1 散斑模型的建立与求解

 $f = u \cdot v,$ (1)

 $f' = u' + v',$ (2)

 $\hat \alpha = \arg \mathop {\min }\limits_\alpha {\left\| \alpha \right\|_0}\, \, {\rm subject\, \, to}\, \, \left\| {D\alpha - {{f'}_0}} \right\|_2^2 \leqslant T,$ (4)

 $\hat \alpha = \arg \mathop {\min }\limits_\alpha \left\| {D\alpha - {{f'}_0}} \right\|_2^2 + \mu {\left\| \alpha \right\|_0}。$ (5)

 $\{ {\hat \alpha _{ij}}, \hat u'\} = \arg \min \lambda \left\| {u' - f'} \right\|_2^2 \\ + \sum\limits_{ij} {{\mu _{ij}}} {\left\| {{\alpha _{ij}}} \right\|_0} + \sum\limits_{ij} {\left\| {D{\alpha _{ij}} - {{\boldsymbol{R}}_{ij}}u'} \right\|_2^2} 。$ (6)

2.2 基于固定字典的图像去噪

 ${\hat \alpha _{ij}} = \arg \mathop {\min }\limits_\alpha {\mu _{ij}}{\left\| \alpha \right\|_0} + ||D\alpha - {x_{ij}}||_2^2。$ (7)

 $\hat u' = \arg \mathop {\min }\limits_{u'} \lambda \left\| {u' - f'} \right\|_2^2 + \sum\limits_{ij} {\left\| {D{{\hat \alpha }_{ij}} - {{\boldsymbol{R}}_{ij}}u'} \right\|} _2^2。$ (8)

 $\hat u' = {(\lambda {\bf{I}} + \sum\limits_{ij} {{\boldsymbol{R}}_{ij}^{\rm{T}}{{\boldsymbol{R}}_{ij}}} )^{ - 1}}(\lambda f' + \sum\limits_{ij} {{\boldsymbol{R}}_{ij}^{\rm{T}}D{\alpha _{ij}}} ),$ (9)

2.3 基于自适应字典的图像去噪

 ${D^*} = \mathop {\min }\limits_{D, {\alpha _j}, j = 1, ..., M} \sum\limits_{j = 1}^M {{\mu _{ij}}} {\left\| {{\alpha _{ij}}} \right\|_0} + \left\| {{y_j} - D{\alpha _{ij}}} \right\|_2^2,$ (10)

 $\{ \hat D, {\hat \alpha _{ij}}, \hat u'\} = \arg \mathop {\min }\limits_{D, {\alpha _{ij}}, u'} \lambda \left\| {u' - f'} \right\|_2^2 \\ + \sum\limits_{ij} {{\mu _{ij}}} {\left\| {{\alpha _{ij}}} \right\|_0} + \sum\limits_{ij} {\left\| {{{\boldsymbol{R}}_{ij}}u' - D{\alpha _{ij}}} \right\|_2^2} ,$ (15)

3.2 仿真结果与分析

 图 2 训练字典。(a)固定字典；(b)自适应字典 Fig. 2 Trained dictionary.(a) Fixed dictionary; (b) Adaptive dictionary

 图 3 各算法的降噪结果。(a) OCT原图；(b)原固定字典算法；(c)原自适应字典算法；(d)中值滤波；(e) Lee滤波；(f)维纳滤波；(g)改进固定字典算法；(h)改进自适应字典算法 Fig. 3 Speckle reduction results of seven algorithms.(a) Original OCT image; (b) Original fixed dictionary algorithm; (c) Original adaptive dictionary algorithm; (d) Median filtering; (e) Lee filtering; (f) Wiener filtering; (g) Improved fixed dictionary algorithm; (h) Improved adaptive dictionary algorithm

 MSE PSNR/dB SSIM EPI OFD 85.0727 28.8329 0.5037 0.4345 OAD 70.4629 29.6512 0.5137 0.4387 中值 97.0321 28.2617 0.6643 0.3464 Lee 101.0175 28.0868 0.7591 0.5692 维纳 72.5142 29.5266 0.6896 0.3438 IFD 69.5172 29.7099 0.8057 0.6842 IAD 46.8668 31.4222 0.7988 0.6569

 图 4 两种改进后字典算法的降噪结果图。(ac)随机选取的三张OCT切片；(df)改进固定字典降噪图；(gi)改进自适应字典降噪图 Fig. 4 Speckle reduction results of two improved dictionary algorithms.(ac) Randomly selected three OCT slices; (df) Noise reduction results by improved fixed dictionary algorithms; (gi) Noise reduction results by improved adaptive dictionary algorithms

 MSE PSNR/dB SSIM EPI 切片97 IFD 47.2845 31.3836 0.8388 0.5962 IAD 42.1495 31.8829 0.8540 0.6051 切片41 IFD 53.8202 30.8213 0.8299 0.5852 IAD 45.1312 31.5860 0.8480 0.6150 切片26 IFD 46.4219 31.4636 0.8306 0.5882 IAD 45.5145 32.0116 0.8468 0.6004 平均值 IFD 49.1755 31.2228 0.8331 0.5899 IAD 42.7332 31.8268 0.8496 0.6068

4 结论

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