The Infrared Astronomical Satellite (IRAS) images with wavelengths of 60 [mu] m and 100 [mu] m contain mainly information on both extra-galactic sources and low-temperature interstellar media. The low-temperature interstellar media in the Milky Way impose a \u22cirrus\u22 screen of IRAS images, especially in images with 100 [mu] m wavelength. This dissertation deals with the techniques of removing the \u22cirrus\u22 clouds from the 100 [mu] m band in order to achieve accurate determinations of point sources and their intensities (fluxes). We employ an image filtering process which utilizes mathematical morphology and wavelet analysis as the key tools in removing the \u22cirrus\u22 foreground emission. The filtering process consists of extraction and classification of the size information, and then using the classification results in removal of the cirrus component from each pixel of the image. Extraction of size information is the most important step in this process. It is achieved by either mathematical morphology or wavelet analysis. In the mathematical morphological method, extraction of size information is done using the \u22sieving\u22 process. In the wavelet method, multi-resolution techniques are employed instead;The classification of size information distinguishes extra-galactic sources from cirrus using their averaged size information. The cirrus component for each pixel is then removed by using the averaged cirrus size information. The filtered image contains much less cirrus. Intensity alteration for extra-galactic sources in the filtered image are discussed. It is possible to retain the fluxes of the point sources when we weigh the cirrus component differently pixel by pixel. The importance of the uni-directional size information extractions are addressed in this dissertation. Such uni-directional extractions are achieved by constraining the structuring elements, or by constraining the sieving process to be sequential;The generalizations of mathematical morphology operations based on the dynamic hit-or-miss transform are presented in this dissertation. The generalized erosion ([gamma]-erosion) bridges traditional erosion and dilation. It also enriches the morphological operators available in the field of signal and image processing. Traditional closing is generalized into [gamma]-closing, which bridges traditional closing and opening. Properties of [gamma]-erosion and [gamma]-closing are discussed. The sieving process is generalized based on [gamma]-closing, and is bi-directional, with the polarity directly related to the parameter [gamma]. The size information extractors of morphological methods and wavelet methods are justified quantitatively using a prototype peak with fixed slope. The non-linearity of the sieving process is analyzed. It is shown that the sieving process can approach an approximate linearity at positions where the input signal has sharp peaks (i.e., the slopes are large). The spatial discriminating properties of the size information extractors are also very important.
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