A Improved Interpolation Technique Based On Solving PDE And Its Application

The problem of constructing a continuously defined function from given discretedata is unavoidable whenever one wishes to manipulate the data in a way that requiresinformation not to be included explicitly in the data. The relatively easiest and in manyapplications often most desired approach to solve the problem is interpolation. Thispaper studies a class of image interpolate ion techniques including linear algorithms andnonlinear algorithms. With the introduction of the edge-preserved interpolationalgorithm based on solving partial differential equation (PDE) and the analysis of itsperformance, the improved algorithm based on solving PDE is brought forward whenthe result of analysis is taken into account.The image acquiring model is studied first, then the aliasing distortion and aperturedistortion resulted from the image acquiring process are analyzed to show theimportance and difficulties of the reconstruction of images with the interpolationtechnique. The classical linear interpolation algorithms, such as nearest neighborinterpolation, bilinear interpolation, Lagrange interpolation, Newton interpolation, B-splines interpolation, and bi-cubic convolution interpolation are investigated. Thenonlinear interpolation methods developed in past decades including the two-channelinterpolation, the edge-directed interpolation, the across-scale pixel correlationinterpolation, the fractal interpolation and the wavelet interpolation and so on are alsostudied. Then the basic idea and theory of nonlinear interpolation are understood. Theclassic linear interpolation methods cannot bring about new high frequency components.On the other hand, the nonlinear interpolation can expand the frequency spectrum torealize the super-resolution and produce the new high frequency components to solvethe problem of blurred edge.The recent research about the PDE theory shows that the PDE method can be usedin image restoration, image segmentation, edge detecting, and image calibration.Although the PDE method is complex during calculating process, it facilitates thepartition of the grid, and the realization of the local nonlinear filtering because itdescribes the image continuous model and the discrete filtering as the continuousdifferential operators. The PDE method can easily denoise and protect the edge with theusing of weighted factor. Especially, the PDE method has unique superiority inprocessing the image, which has broken edge, corner and worse signal continuity. Thepaper introduces the interpolation method based on solving partial differential equation.A new understanding of interpolation is proposed. To overcome the shortcomings of thePDE algorithm proposed by Hao Jiang, some experimental and theoretic analyses aremade. The weighted factor, which is used to predict the orientation of the interpolatedpixel, is studied, and a new operator is presented to ensure its astringency and stability.For the PDE interpolation is a spatial algorithm, it is easy to realize, butcomputationally demanding. So the idea of two-channel interpolation is introduced tosolve this problem. It means that an image is divided into edge areas and flat areas, anddifferent interpolation techniques are employed in different areas to reduce computationcomplexity. The basic knowledge about image analysis and identification technique ispresented, together with the general methods of edge detection. The algorithm usesgradient operator to detect the edge. With the analysis of the characteristics of edge, thealgorithm is amended in the regions, in which the vertical edge or the horizontal edge isincluded, to fit the morphological. Finally, some natural images and simulation images are processed with differentalgorithms. The result shows that the improved PDE algorithm is better than thetraditional interpolation methods in the aspects of vision, MSE and PSNR.