Research On Algorithms Of Gradient Regularization Based Image Reconstruction

In 1975, the first digital camera in the world was born in the Kodak laboratory in New York. Nearly forty years have passed, digital cameras have gained rapid development. People can find digital cameras easily from laptops and cell phones. It has become a new living style to record daily life using photos. However, due to the difference in camera performances, photographers’ camera techniques and shooting situations, the photos people obtained are always with low image quality and poor visual effect. Thus it becomes a new trend for digital cameras to find an easier access to an ideal photo, which utilizes image reconstruction technology to overcome the image degeneration problem in the process of image capture. The study on image reconstruction has high scientific research value and broad application prospects.Image reconstruction is an inverse problem, which aims to estimate the process of image degeneration or to compensate the distortion caused by image degeneration.When there is no prior knowledge about how images are degenerated, the image reconstruction problem becomes an ill-posed problem, which needs a regularization term to make the problem properly posed. Since gradient field contains image structural information and illumination/color variation information, which are the most sensitive information to human vision, gradient-based regularization terms are widely adopted in image reconstruction models. However, in some specific situations, it is hard to obtain valid gradients, which brings great difficulty to the gradient regularization based image reconstruction algorithms.This thesis is focused on the algorithms of gradient regularization based image reconstruction, especially how to effectively apply image reconstruction algorithms when accurate gradient information is hard to obtain. There are two kinds of difficulty may be met during obtaining accurate gradient information. Firstly, there is complete gradient information in the image, but the gradients are mixed with other kinds of gradient signals. Thus a process of gradient classification should be added for obtaining accurate gradient information. The separation of superimposed image is a image reconstruction problem of this type. Secondly, there is not complete gradient information in the image, and it needs to generate the accurate gradient information using the incomplete gradient information. The image super-resolution is a image reconstruction problem of this type. In the cases mentioned above, a regularization term based on valid gradients has become the key factor for generating reconstructed images with high quality. In this thesis, some novel models and algorithms are proposed to establish valid gradient regularization term for superimposed image separation and image super-resolution. The main work of this thesis is as follows:An algorithm is proposed to separate multiple superimposed images by using matched gradients as the regularization term. Based on the investigation of classical gradient extraction techniques, a robust approach is proposed by first registering images with relative motions, and then extracting matched gradients from the registered image pair. To make image registration more accurate, a homography estimation algorithm is proposed by combining keypoint consensus and image similarity in the model of homography estimation. The algorithm can obtain accurate homograhpy results when images are transformed under different transformation degrees and keypoints are contaminated with different percentages of outliers. Based on the regularization term of extracted gradients, the artifacts caused by the original ill-posed separation model are well removed, and the proposed algorithm can produce a clear separation in the superimposed video obtained in real life and in the synthetic superimposed images with severe image transformations.An algorithm is proposed to separate single superimposed image by classifying gradients according to their edge sharpness difference. According to the analysis of the thesis, it is reasonable and feasible to separate a single superimposed image using gradient classification results. An edge sharpness feature GPS(Gradient Profile Sharpness) is designed to make the gradients of transmission image and reflection image separable. Then an MRF-EM(Markov Random Field-Expectation Maximization)model is proposed to classify the gradients of superimposed image, where its data term is based on the distribution of GPS and its regularization term is based on the spatial continuity in gradient classification results. Finally, separated images can be reconstructed using Poisson Solver under the guidance of classified gradients. Compared with previous gradient classification approaches, the proposed algorithm can realize a complete and accurate gradient classification, which can well remove the residuals left in the separated images and keep the tone of separated image consistent with its original superimposed image.An image super-resolution algorithm is proposed by enhancing gradients according to GPS transformation. In the thesis, two gradient profile description models are proposed for precisely describing gradient profiles with different shapes. Then the GPS relationship between different image resolutions is studied statistically, which is applied in proposing two gradient profile transformation models. The proposed gradient profile transformation models can keep profile total energy and profile shape consistent during the transformation. And the gradients in high resolution image can be generated by enhancing gradients in low resolution image using the gradient profile transformation models. With the regularization term of transformed gradients, the proposed algorithm can reduce the artifacts caused by improper gradient enhancement and produce superior HR images with better visual quality and lower reconstruction error as compared to other state-of-the-art works.