Application Of The Research And Improvement On Ridgelet Transform Algorithm

A new analysis method has been proposed at the field of harmonic analysis in applied mathematics in 1980's. It is wavelet analysis, which mainly focuses on wavelet transform. Wavelet transform is a kind of time-frequency analysis method in signal processing and also is a multi-resolution analysis method. It has the ability to represent any part of the signal in both time and frequency domain by a perfect window, which is a window with fixed window size but changeable window shape. Based on this, wavelet analysis has been widely used in mathematics, signal analysis, image processing and analysis, pattern recognition and communications systems.The representation of image is a basic problem in the area of image processing and analysis application. The validity of image representation is that the ability to capture more and more important information in image by less and less data, that is the sparse representation ability. The wavelet transform is perfect only for the point singularity in image, but is slightly less in a valid sparse capacity at two-dimensional or high-dimensional signal representation and processing. Therefore, Candes etc. proposed a new multi-scale geometric analysis method--ridgelet transform, it can effectively deal with a line singularity of singular characteristic of the signal at two-dimensional space. The ridgelet transform effectively represents the line singularity by transforming line singularity characteristics into the point singularity characteristics. Comparing with wavelet transform, ridgelet transform has a better directional feature of the sparse representation. Since the ridgelet theory has been proposed, it is widely used in function approximation, feature extraction, target classification and recognition, image restoration, image denoising, digital watermarking, image coding and so on.In this article we introduce the general theory of wavelet analysis, ridgelet analysis, digital watermark and image compression. And we pay more attention on the mathematical theory and the implementation algorithm of ridgelet transform, as well as its applications in the digital watermark technology and the image multiple description coding. Firstly, considering the image content and the JND (Just Noticeable Difference) model of image in ridgelet domain, we apply the ridgelet transform into digital watermarking technology to propose a local watermarking scheme in the ridgelet domain combining image content and JND model. Experimental results show that the proposed watermarked scheme is robust to noise, cut, JPEG compressing and other intensive attack. After that, a redundant finite ridgelet transform based on blocks(B-RFRIT) is proposed based on the finite ridgelet transform(FRIT). It has been according to that we can get different ridgelet coefficients by increasing or reducing numbers of the projection directions of radon transform and can control the redundancy by changing the size of partitioned image block. Based on the proposed B-RFRIT, we apply it to image multiple description coding, a robust multiple description coding scheme is proposed in my next work. The experimental results show that this program has a good performance on image transfer process and anti-error.