From Particle Mechanics to Pixel Dynamics: Utilizing Stochastic Resonance Principle for Biomedical Image Enhancement

Abstract

There is a noteworthy analogy between the statistical mechanical systems and the digital image processing systems. We can make pixel gray levels of an image correspondence to a discrete particles under thermodynamic noise (Brownian motion) that transits between binary state transition from a weaksignal state to a strong-signal state whereas a noisy signal to the enhanced signal in digital imaging systems. One such phenomenon in the physical systems is stochastic resonance (SR) where the signal gets enhanced by adding a small amount of mean-zero Gaussian noise. A local change is made in the image based upon the current values of pixels and boundary elements in the immediate neighborhood. However, this change is random, and is generated by the sampling from a local conditional probability distribution. These local conditional distributions are dependent on the global control parameter called “temperature” in physical systems (Geman & Geman, 1984). At low temperature the coupling between the particles is tighter means that the images appear more regular and whereas at higher temperature induce a loose coupling between the neighboring pixels and the image appears noisy or blurred image. At particular optimum temperature these particles comes much closer fashion and similarly the pixels of an image got arranged in much closer and leads to noise degradation and further enhances the signal. In this chapter, we discuss the application of the physical principle of stochastic resonance in biomedical imaging systems. Some of the applications of stochastic resonance are signal detection and signal transmission, image restoration, enhancement of noisy or blurred images and image segmentation. Stochastic resonance (SR) is a phenomenon of certain nonlinear systems in which the synchronization between the input signal and the noise occurs when an optimal amount of additional noise is inserted into the system (Gammaitoni et al., 1998). Stochastic resonance is a ubiquitous and conspicuous phenomenon. The climatic model addressing the apparently periodic occurrences of the ice ages by the weak, periodic external signal was thought to be the first theoretical model of stochastic resonance phenomenon, from which the concept of stochastic resonance was put forward (Benzi et al., 1981). Since after the discovery by Benzi, there has been increasingly attracting applications of stochastic resonance in various fields like physics (Gammaitoni et al., 1998), (Anishchenko et al., 1999), chemistry (Horsthemke & Lefever, 2006), biology and neurophysiology (Moss et al., 2004), biomedical (Morse & Evans,