WAVELET-BASED SOLUTIONS FOR PARTIAL DIFFERENTIAL EQUATIONS IN IMAGE PROCESSING

Abstract

Image processing has emerged as a critical science and engineering discipline with applications in the medical imaging field and remote sensing as well as computer vision and multimedia systems. Partial differential equations (PDEs) are useful in many image processing problems, including denoising, deblurring, segmentation, and edge detection problems. The PDE-based models are very powerful in presenting the mathematical basis to explain the image evolution processes, a numerical solution to the model can be very difficult to solve (highly costly to compute) and it is also sensitive to noise. To overcome these shortcomings, wavelet-based techniques have been found to be useful in the solution of PDEs in the image processing field. Wavelets offer multi resolution analysis, which offers effective representation of image properties at varying scales and local areas.