Approximate trigonometric expansions with applications to image encoding

Qurban A. Memon; Takis Kasparis

doi:10.1117/12.242017

7 June 1996 Approximate trigonometric expansions with applications to image encoding

Qurban A. Memon, Takis Kasparis

Proceedings Volume 2751, Hybrid Image and Signal Processing V; (1996) https://doi.org/10.1117/12.242017
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States

Abstract

The objective of data encoding is to transform a data array into a statistically uncorrelated set. This step is typically considered a 'decorrelation' step because in the case of unitary transformations, the resulting transform coefficients are relatively uncorrelated. Most unitary transforms have the tendency to compact the signal energy into relatively few coefficients. The compaction of energy thus achieved permits a prioritzation of the spectral coefficients with the most energetic ones receiving a greater allocation of encoding bits. There are various transforms such as Karhunen-Loeve, discrete cosine transforms etc., but the choice depends on the particular application. In this paper, we apply an approximate Fourier expansion (AFE) to sampled one-dimensional signals and images, and investigate some mathematical properties of the expansion. Additionally, we extend the expansion to an approximate cosine expansion (ACE) and show that for purposes of data compression with minimum error reconstruction of images, the performance of ACE is better than AFE. For comparison purposes, the results also are compared with discrete cosine transform (DCT).

Citation Download Citation

Qurban A. Memon and Takis Kasparis "Approximate trigonometric expansions with applications to image encoding", Proc. SPIE 2751, Hybrid Image and Signal Processing V, (7 June 1996); https://doi.org/10.1117/12.242017

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