In between the Cosmic Microwave Background (CMB) and the instrument there are other sources of radiation, called foregrounds. The foregrounds radiate in the same frequency bands as the background, and cause contamination in the signal of the CMB. To ensure no wrong estimations of the power spectrum, these contaminants must be removed. There are several classes of contaminants, and this thesis has investigated techniques of removing the point sources (class of extragalactic sources), which occupy just a few pixels on the full sky and are located at the small angular scales.
The wavelet filtering technique was used for point source detection, and in particular, new types of wavelets called needlets. The wavelets have good localization properties in both real and harmonic space, and are characterized by an underlying mother wavelet which can be fine-tuned by scaling and translation. These properties make wavelets particularly useful for point source detection. The wavelets can enhance the scales in harmonic space where the point sources are located, such that they are more easily separated from the background. The most used wavelet for detection of non-Gaussianity today is the Spherical Mexican Hat (SMH) wavelet, but needlets are showing promising additional features that make them a possible candidate of succession.