Theory Of Two-dimensional Stochastic Resonance And Applications In Image Processing

Stochastic Resonance (SR), which only occurs in nonlinear systems, is synchronization of nonlinear system with ordered weak stimulus and disordered random perturbation. The concept was raised by R. Benzi in 1981 to address the periodicity of ice ages. Since then it has been widely investigated throughout numerous research areas. Usually, noise is thought to be detrimental. The discovery of SR has led us to realize another aspect of noise:inputting noise can even enhance the signal-to-noise ratio (SNR)! Research shows that under certain circumstance, the input noise can be synchronized with nonlinear system to activate the phenomenon of stochastic resonance, which will highly improve the system's performance. Till now the theory of SR is highly developed and has been applied to one-dimensional (1D) signal processing. However, there is still little work done on two-dimensional (2D) image processing. The thesis mainly focus on establishing theory of SR when input is 2D image rather than 1D signal, and its applications in image de-noising, image fusion, pattern recognition, information retrieval and etc.The theory of Parameter-induced Stochastic Resonance (PSR) has already been successfully applied to 1D signal processing. However, it is quite difficult to extend to 2D case. A major issue is the varied nature of argument. So far all the theories of SR involve one parameter:time t. All stochastic processes evolve with time passing by. However, in static image processing the parameters are coordinates x,y, instead of time t. Since there is no intuitive evolving direction, no existing stochastic theory could be appropriately applied to such problems. Therefore, there exists essential difference between 1D SR and 2D SR. The thesis attempts to expand the 2D stochastic partial differential equation (PDE) in the characteristic direction according to the characteristic method in PDE theory. Then the corresponding Fokker-Planck Equation (FPE) is founded and the static solution and approximate dynamic solution are derived. The dynamic bit error rate (BER) is defined which act as a criteria for parameter optimization. The above procedure has been applied to binary image processing, which works quite well.The system's response speed refers to how fast the system can approach to steady state when input varying. At previous studies the system's response speed is set to be around 3 to make sure that the last sample point of each inputting signal tends to be steadily distributed. The thesis introduces a novel concept of dynamic signal-to-noise ratio (DSNR) to break through the limitation of system's response speed. The statistic properties of averaged output are calculated via theories of local average of random field. Afterwards, the relationship between DSNR and system's parameters a,b is derived, which is then applied to grayscale image processing. Comparing with other mainstream image processing techniques, we have concluded that under certain conditions our proposed method performs better.Image fusion is a technique of merging two or more images taken by different sensors at the same time or by a single sensor at different time, to produce a unique image that carries more information than any of the original ones. It is getting more and more important for large-scale applications, including remote sensing, medical imaging, information classification, security monitoring, and etc. The thesis combines PSR and wavelet transform technique to fuse noisy panchromatic and multi-spectral image to obtain a colored remote sensing image with high resolution. Moreover, A PSR based classifier is derived and applied to pattern recognition of metropolitans, rivers and forests. The experimental results show our classifier outstrips the conventional Bayes classifier.Over exposure is rather annoying when taking photos. However, in some severe light conditions over exposure is inevitable using conventional cameras due to the limitation of dynamic range of image sensor. The over exposed information would be completely lost and unrecoverable. In order to tackle with this problem, the thesis proposes a novel technique which takes the advantage of noise to enlarge the dynamic range of image sensor. It is proved that the visibility of lost information can reach to the peak when specifically added noise synchronized with image sensor system to activate the phenomenon of SR. Four different types of noise are investigated to show the effect of variant distributions to the quality of retrieved information. The experimental results of locally over exposed portrait and over exposed plate number information retrieval are consistent with our theoretic research, which also indicates that the SR based lost information recovery is quite promising.