我們學習到影像雜訊消除應用在細胞神經網路系統中，基於粒子 群最佳演算法，提出一個新的方法設計影像雜訊消除模板以及模板參 數更新。在不需要事先設定細胞神經網路控制模板參數的情況下，它 會設計輸入模板參數並且得到最佳的模板參數，將之用來消除受到雜 訊污染的灰階影像。與一般傳統方法設計的簡單模板大不相同，我們 提出的方法可以配合不同模板得到最佳的模板參數。舉出的例子也可 以發現我們使用的方法在恢復原始圖片上有良好的品質與效率。
4.3 參考 參考 參考 參考文獻 文獻 文獻 文獻
[1] L. O. Chua and L. Yang, “Cellular neural networks: Theory”, IEEE Trans. Circuits Syst., vol. 35, pp.1257-1272, Oct. 1988.
[2] L. O. Chua and L. Yang, “Cellular neural networks: applications”, IEEE Trans. Circuits Syst., vol. 35, pp.1273-1290, Oct. 1988.
[3] K. R. Crounse and L. O. Chua, “Methods for image processing and pattern formation in Cellular Neural Networks: a tutorial”, IEEE Trans. Circuits Syst., vol. 42, pp.583-601, Oct. 1995.
[4] P. Arena, L. Fortuna, G. Manganaro and S. Spina, “CNN image processing for the automatic classification of oranges”, Proc. IEEE Int. Workshop on cellular neural networks and their applications, pp.
463-467, Dec. 1994.
[5] E. Lueder, and N. Fruehauf, “Optical signal processing for CNN's”, Proc. IEEE Int. Workshop on cellular neural networks and their applications, pp. 45-54, Oct. 1992.
[6] P.R. Bakic, B.D. Reljin, N.S. Vujovic, D.P. Brazakovic, and P.D.
Kostic, “Multilayer transient-mode CNN for solving optimization problems”, Proc. IEEE Int. Workshop on cellular neural networks and their applications, pp. 25-30, June 1996.
[7] A. Gacsadi and P. Szolgay, “An analogic CNN algorithm for following continuously moving objects”, Proc. IEEE Int. Workshop on cellular neural networks and their applications, pp. 99-104, May 2000.
[8] A. Paasio, A. Dawidziuk and V. Porra, “VLSI implementation of cellular neural network universal machine”, Proc. IEEE Int.
Workshop on Electronics, Circuits, and Systems, pp. 414-416, Oct.
1996.
[9] K. Halonen, V. Porra, T. Roska and L. Chua, “Programmable analog VLSI CNN chip with local digital logic”, IEEE Trans. Circuits Syst., vol. 2, pp. 1291-1294, 1991.
[10] P. L. Venetianer, T. Roska and L. O. Chua, “Analogic CNN Algorithms for Some Image Compression, Decompression and Restoration Tasks”, IEEE transactions on circuits and systems I:
Fundamental theory and applications, vol. 42, no. 5, pp. 278-284, 1995.
[11] A. Zarandy, F. Werblin, T. Roska and L. O. Chua, “Novel Types of Analogic CNN Algorithms for Recognizing Bank-Notes”, CNNA-94 Third IEEE International Workshop on Cellular Neural Networks and their Applications, pp. 273 - 278, 8-21 Dec. 1994.
[12] A. Zarandy, A. Stoffels, T. Roska, and L. O. Chua, “Implementation of Binary and Gray-Scale Mathematical on the CNN Universal Machine”, IEEE transactions on circuits and systems I:
Fundamental theory and applications, vol. 45, no. 2, pp. 163-168, 1998.
[13] J. Kennedy, R. Eberhart, “Particle swarm optimization”, IEEE International Conference on Neural Networks, vol. 4, pp.1942-1948, 27 Nov-1 Dec 1995.
[14] X. Shenheng, R. S. Yahya , “Boundary conditions in particle swarm optimization revisited”, IEEE Transactions on Antennas and Propagation, vol. 55, NO. 3, pp.760-765, March 2007.
[15] Y. Shi, R. Eberhart, “A Modified Particle Swarm Optimizater”, Proceedings of the IEEE Conference on Evolutionary Computation, pp.69-73, 4-9 May 1998.
出出 席出出 席席 國席 國國 際國 際際 學際 學學 術學 術術 研術 研研 討研 討討 會討 會會 報會 報報 告報 告告告
蘇蘇蘇蘇 德德德德 仁仁仁仁
會議名稱：2009 International Conference on New Trends in Information and Service Science 北京 NISS 研討會
會議日期：2009 年 6 月 30 日 至 7 日 2 日 會議地點：中國北京市友誼賓館
發表論文：Cellular Neural Network for Noise Cancellation of Gray Image Based on Hybrid Linear Matrix Inequality and Particle Swarm Optimization 論文編號：R1S03-256063
論文作者：Te-Jen Su(蘇德仁), Yu-Jen Lin, Chia-Ling Hou 論文頁數：pp.613---617
論文摘要如下：
NISS 2009 研討會所發表的內容有關於使用線性矩陣不等式理論與粒子 群體最佳演算法探討細胞神經網路系統。其研究主題包括輸入與回授模板最 佳化的參數設計、系統穩定問題，討論細胞神經網路在灰階影像雜訊消除上 的應用。基於線性矩陣不等式理論探討系統穩定性，以粒子群最佳演算法求 得在穩定條件下模板的最佳參數，將之用來消除受到雜訊污染的灰階影像。
此次研討會共有七個議題：
(1)網路安全網路安全網路安全、網路安全、、、完整性完整性完整性、完整性、、、隱私與信任議題隱私與信任議題隱私與信任議題 隱私與信任議題
探討網際網路領域中在 Web 安全性裡使用的人工智慧技術、Web 用戶和 Web 代理人的信任和談判、Web 的隱私保存、在 Web 應用過程中的隱私 保存等最新的技術。
(2)城市經營管理的方法學城市經營管理的方法學城市經營管理的方法學議題城市經營管理的方法學議題議題議題
探討有關集中識別標誌、警告預報、政策模擬，專家諮詢和計畫最優化等，
提出不同的計算法則，應用於都市的經營管理鑑定，評價和結合的管理決 策過程中進行改進與分析。
(3)關於知識管理關於知識管理關於知識管理，關於知識管理，，，知識服務和知識的轉移知識服務和知識的轉移知識服務和知識的轉移議題知識服務和知識的轉移議題議題 議題
此議題有關於知識發現和數據采集、以知識為基礎的系統、知識服務、知 識管理和商業情報、知識轉移、決策支持系統、訊息資源共享、知識管理 和Web語義、個性化訊息服務、數字化的圖書館。
(4)在無所不在的電子服務與在無所不在的電子服務與在無所不在的電子服務與在無所不在的電子服務與商業流程開發商業流程開發商業流程開發議題商業流程開發議題議題 議題
如何透過最新技術與方法有效應用於企業界管理，並提升服務品質，在此 針對在電子服務和商業過程之間的會集技術、無線服務應用(例如：RFID，
WiMax) 、無所不在的計算技術與電子服務。
(5)網路與通訊議題網路與通訊議題網路與通訊議題網路與通訊議題
針對網際網路和Web應用、測量和性能分析、多媒體聯網、網路體系架構、
網路操作和管理、基于網路的應用、聯網系統應用程式和服務、下一代網 際網路、光網路和系統、對等和覆蓋網路、QoS和資源管理、近期趨勢和 在計算機網內的發展、通訊的信號處理、無線通信、無線多媒體系統等進 行探討。
(6)金融數據采集議題金融數據采集議題金融數據采集議題金融數據采集議題
探討怎樣使用那些新近發展理論數據采集與金融數據采集。研究內容有:在 當今的金融危機方面的數據采集、在FDM裡監督學習模型/方法、時序數據 分析、在FDM裡的神經網路，決策樹和支持向量機、基於數據采集的預報 模型的股票價格、基於數據采集的預報模型的金融風險、基於數據采集的 金融欺詐察覺模型、金融隱私保護數據采集等研究內容。
(7)語意語意語意P2P網路議題語意 網路議題網路議題 網路議題
探討服務發現和使用基於語義的點對點網路、語義的點對點存儲系統、語 義的對等工作流程管理體制、語義的計算的點對點網路、基於語義的點對 點網路計算的資源搜尋機制和探索法，滿足對更多的對語義的點對點網路 的理論和應用性的研究的需要。
心得 心得 心得心得
透過國際研討會的請益交流，了解國際學術研究最新發展，有助於日後研究 方向之新思維。近年大陸地區對於網路系統研究方面發展迅速，因此，此次 考察特別著重於網路管理系統等議題，期盼能提供授課學生們更多的新知與 研究新方向。
Cellular Neural Network for Noise Cancellation of Gray Image Based on Hybrid Linear Matrix Inequality and Particle Swarm Optimization
Te-Jen Su
Department of Electronic Engineering National Kaohsiung University of
Applied Sciences Kaohsiung 807, Taiwan, R.O.C.
e-mail: [email protected]
Yu-Jen Lin
Department of Electronic Engineering National Kaohsiung University of
Applied Sciences Kaohsiung 807, Taiwan, R.O.C.
e-mail: [email protected]
Chia-Ling Hou
Department of Electronic Engineering National Kaohsiung University of
Applied Sciences Kaohsiung 807, Taiwan, R.O.C.
e-mail: [email protected]
Abstract—In this paper, the technique of noise cancellation for gray image is presented by employing linear matrix inequality (LMI) and particle swarm optimization (PSO) based on cellular neural networks (CNN). A criterion for global asymptotic stability of CNN is presented based on the Lyapunov stability theorem, and the problem of image noise cancellation can be characterized in terms of LMIs. Based on stability conditions of LMI, the parameter of templates are obtained via PSO. The examples are given to illustrate the effectiveness of the proposed method.
Keywords- cellular neural networks, particle swarm optimization, linear matrix inequality, noise cancellation, image
I. INTRODUCTION
Cellular neural networks have been introduced by L.O. Chua and L. Yang [1, 2] in 1988. The most important key point of investigating CNN is how to find the accurate templates. In recent years, the problems of CNN templates design for image processing have received considerable attention.
Genetic algorithm and multilayer CNN were presented to obtain templates for image processing in [3].
A CNN with a particular hysteresis nonlinear cell characteristic was employed for image processing in [5]. In practice, a drawback of CNN templates design is that the templates must be simplified to decrease the time of operation [3] or to analyze dynamical behavior in mathematics easily [4, 5,6].
Recently, there have been several literatures proposed to deal with the stability of CNN by choosing various Lyapunov functions [7-10]. The LMI can now be solved efficiently by the
Particle Swarm Optimization was first presented by the James Kennedy and Russell Eberhart in 1995 [12], inspired by social behavior of bird flocking or fish schooling, it has proven both very effective and quick for a diverse set of
optimization problems.
In this paper, The overall objective of this paper provides a criterion for stability of CNN based on the Lyapunov stability theorem. The problem of gray image noise cancellation can be
characterized in terms of LMIs, and the
optimization parameters of templates are obtained via PSO.
II. PARTICLESWARMOPTIMIZATION(PSO)
In PSO, suppose that the search space is D-dimensional, and then the i-th particle is represented as Xi=(xi1,xi2,K,xiD).
The velocity (rate of the position change) of this particle is denoted as Vi=(vi1,vi2,K,viD). The best previous position of the i-th particle is
represented as Pi =(pi1,pi2,K,piD). In other words, Pi involves the best previous position which has visited (the local best position called pbest).
The index of the best particle among all the particles in the swarm is defined as the symbol (the global best position called gbest). The particles are manipulated according to the following equations: In its canonical form,
follows: iteration t
) (t 1
xid + : position of particle i at iteration t+1 )
(t
xid : position of particle i at iteration t c 1 : acceleration coefficient related to pbest c2 : acceleration coefficient related to gbest
rand()1 : random number uniform distribution U(0,1)
rand()2 : random number uniform distribution U(0,1)
Pid : pbest position of particle i
Pgd : gbest position of particle i
w : inertia weight
III. SYSTEMDESCRIPTION
The associated CNN state equation :
( ) ( ) dynamical behavior of a space-invariant continuous time CNN can be described by following equations:
( ) ( )
In order to simplify the proof of the stability of CNN, we will shift the equilibrium point x of * system to the origin.
Let z(t) =x(t)-x*, Φ(z(t))=y(x(t))-y(x*), system (4) can be represented as
(z(t))
Step 1: In order to prove the global asymptotic stability of the origin of (4), we choose the following positive definite Lyapunov functional:
( ) ( )
t z t 2 ( )( )
sds trajectories of (5) is obtained as( )
Using the Schur Complement Lemma, the inequality (10) holds if and only if
( ) (
A A) (
A A)
0 matrices, (11) can be rewritten as( )
M M 0In the above, we have demonstrated that (13) is the criterion of the global asymptotic stability of
Step 2: The uniqueness of the equilibrium point
0
∗=
z is proved by contradiction method.
Consider the equilibrium equation of (5)
( )
z -A( )
z 0 (15) can be expressed as the following inequality( )
z*[
A A-I] ( )
z* 0Consider the criterion for the global asymptotic stability of CNN (13), it implies that
because equation (17) contradicts with equation (18), the equilibrium point z* =0 of (5) is unique.
So far, the criterion of uniqueness and global asymptotic stability of the equilibrium point of CNN has been derived above. In other words, the template “A” is obtained already according to (13). Now, we will design template “B” of CNN to achieve desirable output at steady state.
The dynamical behavior of CNN in (4), the equilibrium equation of (4) is show as
( ) ( )
By using the property of saturation nonlinearity, (19) is rewritten as the following inequalities
1
IV. LMIANDPSOBASEDONCNNTEMPLATE
LEARNING
Figure 1. Training system
If the following LMIs are existence, then the templates of the CNN for the image
reconstruction would be solvable.
1. A+A-I<0
In this paper, we use row-wise packing scheme to describe the dynamical behavior of cell, training samples with size 32 by 32, and the sphere of influence of the radius r=1.
V. EXAMPLE
We present an example polluted by 10% of noise density interference and using CNN with LMI and PSO approach for image noise cancellation.
and its corresponding desired image.
Figure 2. Training sample (a) desired image (b) corrupted image with 10% noise
TABLE I. PSO PARAMETER SETTINGS
The number of swarm size 15 The maximum position Xmax 1 The maximum velocity Vmax 10 Acceleration coefficient c1 1.4 Acceleration coefficient c2 1.2
Inertia weight w 0.8
Iterations 300
We obtain the templates A10%, A 10%, A 10%ˆ1 ˆ0
and B10%, B 10%, B 10%ˆ1 ˆ0 as follows:
Example: We consider the 128*128 images in Figure.3 (a) and Figure.4 (a) which were also noise images and polluted by the salt and pepper 10% noise in Figure.3 (b) and Figure.4 (b) The results of using LMI and PSO based on CNN method in Figure.3 (c) and Figure.4 (c).
Figure 3. The results of using LMI and PSO based on CNN method (10% noise).
Figure 4. The results of using LMI and PSO based on CNN method (10% noise).
Figure 5. Iterations of LMI-PSO-CNN Training
In order to calculate the performance of the presented method under different levels of noise ratio, we introduce the Peak Signal to Noise Ratio (PSNR) as
( )
2m
1 i
m
1 j
ij
2 yij y
m
MSE 1
∑∑
= =
−
= ~ ˆ (21)
MSEdB 10 255
PSNR
2
log10
= (22)
where y~ij is the pixel of the ideal image, yˆij is the pixel of the reconstruction image at the output of CNN.
TABLE II. PSNR OF LMI AND PSO-CNN FOR 10%NOISE
Figure.3 Figure.4 Salt and Pepper 12.1253dB 11.5312dB LMI and PSO-CNN 32.8353dB 31.1027dB
VI. CONCLUSION
In this paper, a solution to the templates design of CNN for noise cancellation of gray image is proposed. It is shown that the design problem can
be transformed into LMIs, and the optimization parameters of templates are obtained via PSO.
Hence, we have presented an effective algorithm to the templates design for gray-scale image reconstruction using LMI and PSO based on CNN.
In the future, the problem of robust templates design should be considered under the uncertain CNN systems.
REFERENCES
[1] L. O. Chua and L. Yang, “Cellular neural networks: theory”, IEEE Trans. on Circuits and Systems, Oct. 1988, 35, pp. 1257-1272.
[1] L. O. Chua and L. Yang, “Cellular neural networks: theory”, IEEE Trans. on Circuits and Systems, Oct. 1988, 35, pp. 1257-1272.