11-10-2012, 05:31 PM
DCT-BASED IMAGE COMPRESSION
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ABSTRACT
The advantages of DCT compression are based on the fact that most natural images have sparse edges. Hence, most
blocks contain primarily low frequencies, and can be represented by a small number of coefficients without
significant precision loss.
Edges are problematic since are associated with high spatial frequency. Consequently, the DCT at blocks where the
edges pass has high-amplitude coefficients at high frequencies, which cannot be removed without significant
distortion. This effect was seen on the coin image, where small number of coefficients resulted in very significant
distortion of the edges.
Images containing non-sparse edges, such as the standard MATLAB image of an integral circuit (IC), are very
problematic for such compression method, since they primarily consist of edges.
The compression algorithm can be significantly improved if the coefficients selection would be adaptive, i.e. in each
DCT block we would select a different number of coefficients with the largest amplitude. Thus, smooth regions of
an image can be represented by a small number of coefficients, whereas edges and high-frequency textures would be
represented by large number of coefficients. This will solve the problem of edges, whilst leaving the algorithm
efficient.
The number of coefficients required for edge representation can be reduced if the idea of overcomplete base is used.
Using some overcomplete basis for geometry representation (e.g. different types of edgelets, ridgelets and other
geometry encoding wavelets proposed by Mallat and Donoho) it would be enough to take only several coefficients
in order to represent an edge.