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Visual information transmitted in the form of digital images is becoming a major method of communication in the modern age, but the image obtained after transmission is often corrupted with noise. The received image needs processing before it can be used in the applications. Image denoising involves the manipulation of the image data to produce a visually high quality image. This thesis reviews the existing denoising algorithms, such as filtering approach, wavelet based approach, and multifractal approach, and performs their comparative study. Different noise models including additive and multiplicative types are used. They include Gaussian noise, salt and pepper noise, speckle noise and Brownian noise. Selection of the denoising algorithm is application dependent. Hence, it is necessary to have knowledge about the noise present in the image so as to select the appropriate denoising algorithm. The filtering approach has been proved to be the best when the image is corrupted with salt and pepper noise. The Partial differential equation approach finds applications in denoising images corrupted with Gaussian noise. In the case where the noise characteristics are complex, the multi fractal approach can be used. A quantitative measure of comparison is provided by the signal to noise ratio of the image. Aim of the project is to reduce the speckle noise from the medical images by retaining most of the information, using fourth order partial differential equations and comparing the results with second order partial differential equation method, that is best suitable for a medical practitioner or a doctor to diagnose well by comparing this denoised image with the obtained.