Study On Color Filter Array Interpolation Based On Two-dimensional High Order HMM

Image is the primary media of communication. With the rapid development of science and technology, people's demand for the image quality is also increasing. Compared with low resolution image, high resolution one can provide a clearer picture and a better view. However, due to the factors of the manufacture techniques of image sensor and imaging environment, it is difficult for the collection pictures to satisfy people's requirement of image quality. Given the technical bottleneck exists in hardware schemes, signal processing based image interpolation technique has become one of the ideal solutions, which is expected to breakthrough the limitations of the hardware schemes. The image interpolation technique is more and more widely applied in medical and public health, remote sensing, public security and other areas, and it is paid extensive attention from scholars at home and abroad.This thesis makes a deep research on two-dimensional high order hidden Markov model based color filter array interpolation methods, mainly on probability calculation, path backtracking, and parameters estimation, as well as statistical properties of natural images, non-local similarity, and so on. The major contributions are following:(1) To avoid the disadvantages of the classical hypothesis of hidden Markov model, definition and structure are given of nth-order hidden Markov model related to the observations. Forward algorithm is studied, and the probability of the observation sequence given a particular model can be calculated using the forward algorithm. By generalizing Baum-welch algorithm, parameter estimation equations for the model are derived.(2) To overcome the shortages of the classical hypothesis of two-dimensional discrete hidden Markov model, a novel model called two-dimensional discrete 3×4 order hidden Markov model is proposed. This paper defines the structure of the proposed new model in which the observation symbol probability depends on not only current state but also immediate horizontal, vertical and diagonal states, and in which the state transition probability depends on not only immediate horizontal and vertical states but also immediate diagonal state. The three fundamental problems of the model are studied, including probability calculation, path backtracking and parameters estimation. Several algorithms solving the three basic questions are theoretically derived by exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1×2 order hidden Markov model. Compared with two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed new model, therefore the proposed model theoretically can more accurately describe some practical problems.(3) A novel model referred to as two-dimensional continuous 3×3 order hidden Markov model is put forward to avoid the disadvantages of the classical hypothesis of two-dimensional continuous hidden Markov model. This paper presents three equivalent definitions of the model, in which the state transition probability relies on not only immediate horizontal and vertical states but also immediate diagonal state, and in which the probability density of the observation relies on not only current state but also immediate horizontal and vertical states. The paper focuses on the three basic problems of the model, namely probability density calculation, parameters estimation and path backtracking. Some algorithms solving the questions are theoretically derived, by exploiting the idea that the sequences of states on rows or columns of the model can be viewed as states of a one-dimensional continuous 1×2 order hidden Markov model. Simulation results further demonstrate the performance of the algorithms. Because there are more statistical characteristics in the structure of the proposed new model, it can more accurately describe some practical problems, as compared to two-dimensional continuous hidden Markov model.(4) Image demosaicing is the process by which from a single CCD sensor recording only one color sample at each pixel, a full color information per pixel can be inferred. Most image demosaicing methods assume the high local spectral correlation in estimating the missing color components. However, such an assumption may fail for images with high color saturation and sharp color transitions. Meanwhile, self-similarity, which means that the pixels at different locations may resemble with each other, is a fundamental property of an image. In this paper, the non-local similarity information provided by an image itself is made use of demosaicing on the McMaster dataset with lower local redundancy. Experimental results show that the presented algorithm is able to improve the PSNR, sharpen texture and edge of the image and lead to higher visual quality of reproduced color images.(5) Two-dimensional high order hidden Markov model is an effective machinery of characterizing sample dependencies in high order Markovian processes for image processing applications. We propose two kind of adaptive color filter array interpolation techniques based on two-dimensional continuous 3×3 order hidden Markov model and two-dimensional discrete 3×4 order hidden Markov model. The two-dimensional high order hidden Markov models incorporate the statistics of high resolution images into the interpolation process and the state estimation exploits high-order statistical dependency between pixels. Experimental results show that the proposed algorithms are able to improve the CPSNR, sharpen edge and texture and lead to higher visual quality of reconstructed color images.In summary, on the basis of the basic theory of two-dimensional hidden Markov model and the color filter array interpolation algorithms, and making the full use of the variance of color differences, the statistical properties of natural images, and the non-local similarity, we propose two novel two-dimensional high order hidden Markov models and four novel color filter array interpolation algorithms. Compared with the existing methods, our proposed methods can achieve better high resolution recovery.