Research On Improved Curvelet Transform And Its Applications On Image Processing

Wavelet transform has been established as an excellent method of time-frequency analysis for non-stationary signals. 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, but also has many shortages, so, research on improved curvelet transform and its application of image processing is of far reaching importance.This paper firstly introduces the basic knowledge of Curvelet transform, and gives an improved curvelet algorithms, then, analysis the curvelet coefficients from two aspects: structure, statistic and characteristic. Then the applications of improved transform are discussed from three aspects of image processing. At first, we combine the improved curvelet transform and embedded wavelet zeros tree coding, put forward an embedded wavelet zerotree coding based on improved curvelet. It can compress images at any ratios. This algorithm has better performance especially for the images with linear edges. Secondly, a digital image watermark embedding and extracting algorithm is presented based on the improved curvelet transform which can efficiently represent image with linear singularities, which make the watermark information embedded in special coefficients. Different noises with different SNR are added to the watermarked image in the experiments and the results prove robustness and transparency. The experiments are carried out in this paper respectively towards the two aspects of applications of improved curvelet transform in the image processing mentioned above. The experimental results demonstrate the effectiveness of the improved curvelet theory in the applications of image processing.