Multi-resolution Multi-directional Transform In Image Processing Applications

Multiscale Geometric Analysis is a booming hot research topic in recent years, which aims to obtain flexible, fast and effective signal processing algorithms through efficient approximation and characterization for the inherent geometric structures of high-dimensional data. Ridgelet, Curvelet and Contourlet, as its two-dimensional cases, represent a new type of harmonic transforms with multiresolution, locality, directionality, anisotropy and fixed basis elements. This thesis mainly focuses on ridgelet, curvelet and contourlet. Includes:1) The theories of ridgelet and curvelet are elucidated in detail. The ridgelet transform is a new directional multi-resolution transform, which is more suitable for describing the signals with high linearity dimensional singularities. One discrete version of ridgelet transform called finite ridgelet is specific studied. Then we study a discrete version of curvelet transform based on fourier transform.2) Improve the finite ridgelet algorithm. Finite ridgelet transform is only suitable for images of prime-pixels length, which is a limitation of its application in image processing. We improve the finite ridgelet algorithm and a new digital implementation of ridgelet transform that is suitable for images of dyadic length is proposed. This method not only expands the application of finite ridgelet transform, but also simplifies the algorithm. Then we use it in curvelet and gain a low redundancy curvelet. We compare the new method with traditional curvelet transform based on fourier transform in image denoising experiments. Although it performs a little worse than the traditional one, considering its low redundancy and simple algorithm, it is still useful.3) The theory and implementation of contourlet transform are studied in detail. Then we point some limitations of contourlet transform caused by the downsampling, such as the properties of shift variance and frequency scrambling. At last we give a brief introduction of non-sampled contourlet transform.4) A novel method for texture feature extraction is proposed based on completed non-sampled contourlet. This approach extracts the distribution of directional subbands of completed non-sampled contourlet coefficients by gauss mixture model. Then, we calculate L2distance between the query image and the images in database and rank them to gain the query results. Compared with other...