Research On Curvelet Transform And Its Applications On Image Processing

Wavelet transform has achieved great development in signal processing, which profits from its time-frequency analysis and near-ideal ability to represent one dimension function of bounded variation. It's a pity that wavelet analysis can't take full advantage of geometrical characteristic (line singularities, plane singularities) of the data to get the sparse representation of the function. Curvelet transform can provide near-optimal representation of objects with line singularities and plane singularities. So, research on curvelet transform and its application of image processing is of far reaching importance.This paper firstly introduces the basic knowledge of multiscale geometric analysis and curvelet theory; then studies and analysis the implementation procedure of curvelet transform; analysis the curvelet coefficients from three aspects: structure, statistic and characteristic; realizes two applications of curvelet transform in image processing field.First, put forward a digital image watermark algorithm based on curvelet transform The main design work of the algorithm contains quadrilateral: (1) preprocess the watermark; (2)choose proper embed position; (3)watermark embed algorithm; (4)blind extract algorithm. Next, test the visibility and the robustness of the watermark algorithm, and compare the test results with results of the wavelet domain based watermark algorithm. The results show that curvelet domain based watermark algorithm guarantees the invisibility, in the meanwhile has great robustness It's better than wavelet domain based algorithm.Second, put forward a digital image fusion algorithm in the curvelet domain Firstly, design the implementation of curvelet domain based image fusion algorithm; secondly, experiment with various kinds of image fusion rules, compare the experiment results with the results of wavelet domain based image fusion algorithm, the cuvelet domain based algorithm received better fusion effect; thirdly, choose best combination rule to realize the curvelet algorithm, imply it to the remote sensing image, multi-focus image and medical image fusion, which also achieve satisfactory effect.