Researches On Basis Function Representation Of Image Information

Image representation plays an important role in image processing technology. Based on generative image models, an image is represented as a linear combination of a set of basis functions, simulating the image generation process. By projecting the original image onto the space of basis function, the projection coefficients are capable of revealing latent structures of the image which facilitates image recognition, denoising as well as compression. The capability of characterizing image information largely depends on the selection of basis functions. Relative to the traditional way of predetermining basis functions, basis functions generated by learning algorithms are adapted to image characteristics and hence more efficient in image representation. Basis function-based image representation is currently a frontier research in the field of image processing, involving multiple disciplines such as statistics, geometry, visual physiology etc.Based on image generative model, in combination with independent component analysis model and wavelet model, the basis function representation of image information as well as its key problem are studied in this thesis. By representing images as projection coefficients in high dimensional space expanded by basis functions, statistical characteristics of projection coefficients are studied. The basis functions under certain constrains are derived and further used to describe complex structure information in image. In addition, learning algorithms for constructing the adaptive image basis functions are studied.The main work is as follows.(1) The research status of basis functions construction method in image information representing is summarized. The advantage and disadvantage of Fourier transform, wavelt and independent component analysis with respect to basis function-based representation is analyzed. The research route of image information represention efficiency is derivated from statistical character and condition restricted of basis function and projection coefficients.(2) Projection coefficients of image information in basis function space is non-gaussian in independent component analysis model. The high-order statistical features is used in characterize non-gaussian feature. The combined moments of second-order and higher-order statistical features is proposed to describe the projection coefficients probability distributing characteristic, which used in multi class texture classification.(3) Locally non-negative mean field independent component analysis is proposed, which basis function is combined with local non-negative restrict in mean field independent component analysis model. Sparse basis function is derived. Robust recognition performance is obtained when used to objects recognition. (4) Sparse wavelet model of adaptive basis function is proposed, which combined basis construction of independent and wavelet. The adaptive wavelet basis function is constructed from Lattice structure. The sparsity restrict is imposed on the wavelet coefficient. The studying of basis function is translated to optimization problem of low dimention of wavelet basis function and the incertitude is reduced in basis function estimation. The description ability of image structure is enhanced efficiency.