Image Processing and Fourier — Wavelet Methods
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The image processing and signal analysis whose ingredients are modelling, transforms, smoothing and sharpening, restoration, encoding (image data compression, image transmission, feature extraction), decoding, segmentation, representation, archiving and description, have played a vital role in understanding the intricacies of nature, for providing comforts, luxuries and pleasure to all of us, and even probing mission of a space-craft. Image processing is used in telecommunications (telephone and television), photocopying machine, video camera, fax machine, transmission and analysis of satellite images, medical imaging (echography, tomography and nuclear magnetic resonance), warfare, artificial vision, climatology, meteorology and film industry for imagery scenes. In short, it is one of the most important disciplines for industrial development and unveils the secrets of nature. Different kinds of techniques and tools like Fourier series, Fourier transform, Walsh-Fourier transform, Haar-Fourier transform, Hotelling transform, Hadamard transform, entropy encoding and, more recently, wavelets, wavelet packets, and fractal methodology have been used to tackle the problems of this field. It is difficult to say authoritatively which method is superior to the other in a particular situation. However, a combination of the wavelets and fractal methods promises for a great future. This chapter comprises five sections, namely, image model and methods of image processing, classical Fourier analysis, wavelet techniques in image processing, Fractal image processing and problems.
KeywordsCompression Ratio Discrete Fourier Transform Wavelet Coefficient Image Compression Scaling Function
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