Research And Applications Of Ridgelet Transform

Wavelet transform has been established as an excellent method of time-frequency analysis for non-stati- onary signals. It can be used to describe the signals with point singularities effectively. However, for the sign- als with singularities in high dimensional space, Wavelet analysis loses its advantages. Under this situation, the Ridgelet transform was introduced as a new multiscale representation for functions on continuous spaces that are smooth apart from discontinuities along lines. It can perfectly express images having straight edges with sparse coefficients and can be widely used in the field of image processing.This paper firstly introduces the basic algorithms of Ridgelet transform, and gives their implementation. Then the applications of Ridgelet transform are discussed from three aspects of image processing. At first, a digital image watermark embedding and extracting algorithm is presented based on the multiscale Ridgelet transform which can efficiently represent image with linear singularities. The digital image with curvilinear edges or texture is partitioned into small pieces which are then treated by Ridgelet transform. And the watermarks are embedded in some special coefficients. Different noises with different SNR are added to the watermarked image in the experiments and the results prove robustness and transparency. Secondly, zerotree coding which is one of the most efficient still image compression methods is applied to the lossless image compression based on Ridgelet transform. This compression algorithm inherits the successive approximation thought of the wavelet zerotree coding algorithm by quantifying Ridgelet coefficients reasonably and effectively. It can compress images at any ratios. This algorithm has better performance especially for the images with linear edges. At last, the signal model of Ground Penetrating Radar (GPR) is analyzed and the Ridgelet theory is applied into the GPR signal processing. The direct wave noise and Gaussian white noise are suppressed in Ridgelet domain and the effectiveness of the algorithm is proved by simulations based on two groups of real measurement data. The experiments are carried out in this paper respectively towards the three aspects of applications of Ridgelet transform in the image processing mentioned above. The experimental results demonstrate the effectiveness of the Ridgelet theory in the applications of image processing.