The Bayesian least squares-Gaussian scale mixtures (BLS-GSM) algorithm developed by Portilla et al. applied a maximum a posteriori (MAP) estimation based on exponential marginal prior. Simoncelli published a research paper on the Bayesian denoising process, and Mihcak et al. proposed an algorithm which uses hidden Markov models (HMM) to obtain the variance of signal and therefore, to denoise with Bayesian estimation. Malfait and Roose further exploited a methodology to realize the Bayesian approach by applying the Markov random field and Crouse et al.
Lee, likewise, proposed a two-step empirical Bayesian estimation which estimates the variance of signal from the neighbors of an observed pixel and applies the standard linear least squares (LLS) solution. Robbins proposed an empirical Bayesian framework to estimate Gaussian noise. Traditional denoising algorithms have employed the additive white Gaussian noise modeling to account for the second source of noise, which is signal-independent. The two predominant sources of noise in digital image acquisition are (a) the stochastic nature of the photon-counting process at detectors, and (b) the intrinsic thermal and electronic fluctuations of the acquisition devices. The aim of this study is to model and remove the noise in a low-count image. Therefore, these applications acquiring images by photon counting have extremely low signal to noise ratio. In many image applications such as fluorescence microscopy and astronomy, only a limited number of photons can be collected due to various physical constraints such as a light source with low power to avoid phototoxicity, and short exposure time. Owing to the development of image sensor hardware, increased spatial resolution has resulted in a decreased sensor pixel size, which causes the expansion of the photon noise effect. Such demands have consequently led to the advancement of image sensors such as the charge coupled device (CCD) and the complementary metal oxide semiconductor (CMOS). Image acquisition and processing is also common in medical technology and the service industry.
We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach.ĭigital images are prevalent in our lives as a result of advances in multimedia, internet, computers, and wide spread of portable imaging devices such as consumer digital cameras and camcorders. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain.
We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints.