Image Interpolation Method Based On Wavelet Transform

The theory of wavelet analysis is a new disciplines,and a hot pointsof research in international and domestic.and a hot points of research ininternational and domestic .achieves the attention in all over the world oflate years.It is also a pop-researching field internationally and arousesextensive attention and upstairs recognition in science and technologyfield. The development of wavelet analysis forcees the development ofmany others study and field. Depending on its unique advantage, thewavelet theory gaines extensive attention in digital image processing.This paper mainly research the application of the theory of wavelet andthe theory of random fractal geometry .in the field of the digital imageprocessing. The random fractal geometry and wavelet theory are usedfor analysis the surface geometry and image processing,a effectivealgorithm is proposed.sfsIn the field of the digita image processing,Image interpolationis one of the most and basal technique,the magnifying and theresolution enhancement can be realized by image interpolation,which is very important practically in the sharpness processingand the 3-Ddisplaying.Image interpolation is an important problemClassical image interpolation Method,Such as replication,bilinearinterpolation and bicubic spline interpolation and so on,are all based onNyqusit sampling theory.They approach to perfect low pass filterSo high frequency parts are lost,and the quality of image isreduced .In this way the edge of image become blur.Moreover ,the edgesof image include the most important information in the image,and it isthe one of most important characters in image interpolationmethods all pay attention to improving the edge to impove thevision effect of the whole image.After an image is decomposed by wavelet with themultiresolutionanaysis, three high frequency sub-images and one low frequency sub-image are gained . In the high frequency one , the values ofmost pixels are close to zero,which contains the information on textureand edge and so on , While the low frequency one is the bestapproach ofthe original image on certain scale and resolution,whichcontains ninetypercent of the energy of original image.Imageinterpolation can void dealing with the noise at the same time enlarged;Texture image exists in everywhere.Pentlan proved that greylevel of image is met isotropic Fractional Brownian Model(FBM) bystudied the texture of natural image.Therefore, Based on self-similarprinciple of fractal geometry,we can obtain the fractal parameterby studying the fractal character of image,and that can improvethe resolution and also maintain the texture of an medical image beapplying fractal interposition.in contrast, using random fractal method toenlarge images can get better visual quality by adding more detailto the images.because fractals have infinite details.Based on these facts,in this paper ahybrid approach of imageinterpolation combining the wavelet with fractal is proposedFirstly,an imge is decomposed by wavelet,three high frequencysub-imagesand one low frequency sub-image are gained.thenrepectively,the three highe frequency su-bimages is reconstructed,the f Hsub-image is gained;the low frequency sub-image isreconstructed, f Lsub-imageis gained too.Image interpolationsteps as the follwing:After an image is decomposed by wavelet,three high frequencysub-images and one low frequency sub-image are gained.In thehigh frequency one,the values of most pixels are close to zero,whichcontains the information on texture and edge and so on,while the lowfrequency one is the best approach of the original image on certainscale and resolution, which contains ninety percent of the energyof original image1) λ ?Cubic convolution is applied to the f Lsub-image;2) Random fractal interpolation is applied to the f Hsub-image;3) Finally,the interpolation image consists of two parts ie f Limageand f Himage.The numeric experiments prove the validity of this method. Thismethod can achieve preferable results to some image data such asnutrual scenery, human picture and remote sensing image. Comparedwith the traditional methods used in the image processing. The resultsshow that the method can improve the smoothness effect of traditionmethods greatly and keep the edges of interpolation image still sharpand smooth.This approach offers advantages of taking into account thecorrelation of the whole image, keeping fine details of image andavoiding the sawtooth effect and smoothing effect associated withraditional image interpolation techniques. The experimental results showthat our approach is able to get higher PSNR than existing Interpolationmethods in most cases...