Using computer algebra to perform image compression with wavelet transform and SVD

摘要

Computer Algebra Software, especially Maple and its Image Tools package, is used to develop image compression using the Weibull distribution, Wavelet transform application and Singular Value Decomposition (SVD). For prototyping of the image compression process, Maple packages, Linear Algebra, Array Tools and Discrete Transform are used simultaneously with Image Tools image processing package. The image compression process implies the realization of matrix computing with high dimension matrices, and Maple software develops those operations easily and efficiently. Some image compression experiments are done, and the matrix dimension for minimum information needed to store an image is shown clearly, also the matrix dimension of redundant information. Implementation of algorithms for image compression in other computer algebra systems such as Mathematica and Maxima is proposed as future investigation path. Also it is proposed the use of curvelet transform as a tool for image compression.