Study On Multiscale Analysis For Image Processing

Wavelets have found wide applications in image processing due to the time-frequency localization and multiscale decomposition property. It has been adopted as a key technique in the new still image compression standard JPEG-2000. The denoising of a natural image is a classic problem in signal processing. The wavelet transform has become an important tool for this problem due to its energy compaction property. The Multiscale Geometric Analysis(MGA) is name for a number of independent developments in computational harmonic analysis. Multiscale Analysis and its application in image processing are investigated in detail in this dissertation. The main work can be summarized as follows:1. For image denoising, the basic principles and all kinds of shrinkage function's selection and evaluation are discussed. A denoising algorithm based on adapted shrinkage function combined with spatial filter is proposed. Experiments results show the combined denoiser is superior to the single wavelet-based denoiser.2. The balanced multiwavelet and its application in image denoising are studied. For low-pass matrix filter P(ω), the orthogonal matrix R is selected to ensure the constant signal as a characteristic signal matrix filter of balanced low-pass matrix filter. As an application, the OPTFR multiwavelet is balanced, then employ adaptive,subband dependent threshold to the detail subbands. Compared with other multiwavelets, the proposed method presented here gives a better result.3. A denoising method based on the dual-tree complex wavelet transform(DT-CWT) is proposed. The DT-CWT possesses approximate shift invariance and good directional selectivity, at the same time, it can be perfect reconstructed. Each scale of the 2-D DT-CWT transform gives rise to subbands oriented in six distinct directions. The denoising method adopt a bivariate shrinkage function. Experiments results show that the proposed method is an effective method.4. A method based on the DT-CWT for image fusion is proposed. First, the registered images are transformed to wavelet domain using DT-CWT. Then a simple "maximum selection" scheme is applied to the magnitude of the DT-CWT coefficients to generate the combined coefficient map. Finally, the inverse DT-CWT is applied to the combined coefficient map to produce the fused image. This fusion method gives better result than PCA method, wavelet fusion and Laplacian pyramid method.5. The sparse approximation for image is discussed, including Fourier nonlinearapproximation, wavelet nonlinear approximation, and the approximate performance comparison among various multiscale methods. Wavelet analysis can give more "sparse" expression than Fourier analysis in piecewise smooth signal or bounded variance function. New multiscale methods can give better performance in approximating multivariate function in high-dimension space than wavelet analysis.6. A method for texture classification is presented based on Brushlet and dyadic wavelet. This method uses the ideas of moment and anisotropic information detection, combined with information detection characteristic of brushlet and edge detection characteristic of dyadic wavelet transform. Lastly, the SVMs is used to classify texture images. All the textures in Brodatz is classified by this method and a group of detailed experimental data is given in the thesis.7. The application of ridgelet and curvelet in image application is discussed. Ridgelet can effectively deal with line-like and hyperplane-like singularities. A method based on monoscale ridgelets for image fusion is proposed. Experimental results show the result is superior to that of wavelet's. For singularities alone curves, curvelets can give sparse representation. By simple thresholding rule, the curvelet denoising rivals sophisticated techniques of the wavelet denoising.