Approximate trigonometric expansions with applications to image encoding

Qurban Memon, Takis Kasparis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


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 prioritization 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).

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsDavid P. Casasent, Andrew G. Tescher
Number of pages10
Publication statusPublished - 1996
Externally publishedYes
EventHybrid Image and Signal Processing V - Orlando, FL, USA
Duration: Apr 8 1996Apr 8 1996

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering


OtherHybrid Image and Signal Processing V
CityOrlando, FL, USA

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Approximate trigonometric expansions with applications to image encoding'. Together they form a unique fingerprint.

Cite this