Image Compression by Using Haar Wavelet Transform and Singualr Value Decomposition
Independent thesis Advanced level (degree of Master (Two Years)), 15 credits / 22,5 HE creditsStudent thesis
The rise in digital technology has also rose the use of digital images. The digital imagesrequire much storage space. The compression techniques are used to compress the dataso that it takes up less storage space. In this regard wavelets play important role. Inthis thesis, we studied the Haar wavelet system, which is a complete orthonormal systemin L2(R): This system consists of the functions j the father wavelet, and y the motherwavelet. The Haar wavelet transformation is an example of multiresolution analysis. Ourpurpose is to use the Haar wavelet basis to compress an image data. The method ofaveraging and differencing is used to construct the Haar wavelet basis. We have shownthat averaging and differencing method is an application of Haar wavelet transform. Afterdiscussing the compression by using Haar wavelet transform we used another method tocompress that is based on singular value decomposition. We used mathematical softwareMATLAB to compress the image data by using Haar wavelet transformation, and singularvalue decomposition.
Place, publisher, year, edition, pages
2011. , 60 p.
Multi resolution analysis; Haar wavelet transformation(MRA); Average and difference method; Singular value decomposition(SVD).
IdentifiersURN: urn:nbn:se:lnu:diva-11467OAI: oai:DiVA.org:lnu-11467DiVA: diva2:412929
Subject / course
Mathematics and Modelling, Master Programme, 120 credits
2010-09-27, B2034, Växjö, 18:45 (English)
UppsokPhysics, Chemistry, Mathematics
Asekritova, Irina, Lektor
Nillsson, Börje, Professor