TY - GEN

T1 - Approximate trigonometric expansions with applications to image encoding

AU - Memon, Qurban

AU - Kasparis, Takis

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0029766744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029766744&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029766744

SN - 0819421324

SN - 9780819421326

T3 - Proceedings of SPIE - The International Society for Optical Engineering

SP - 26

EP - 35

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Casasent, David P.

A2 - Tescher, Andrew G.

T2 - Hybrid Image and Signal Processing V

Y2 - 8 April 1996 through 8 April 1996

ER -