21-09-2012, 03:09 PM
A Fast Block-Pruned 4x4 DTTAlgorithm for Image Compression
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Abstract
The Discrete Tchebichef transform (DTT) is a
linear orthonormal version of the orthogonal Tchebichef
polynomials, which is recently used in image analysis and
compression. This paper presents a new fast block-pruned 4x4
DTT algorithm which is suitable for pruning the output
coefficients in block fashion. The principle idea behind the
proposed algorithm is the utilization of the
distributed-arithmetic and the symmetry properties of 2-d DTT
in order to combine similar terms of the linear combination of
each computed pruned output. As well as, some trivial
multiplications are represented by shifts or add-shift operations
to reduce the number of required computations. The proposed
algorithm requires the smallest computation complexity with
respect to other recently proposed algorithms. Different
block-pruning sizes are considered in the comparative analysis
of the proposed algorithm vs. others. Furthermore, the
experimental results show that the DTT is a good alternative for
the Discrete Cosine Transform (DCT) in image compression
especially for artificial diagrams images.
INTRODUCTION
Huge amounts of image data such as digital photographs,
webpage pictures, and videos are created and transmitted via
the internet. Due to the limited data storage and network
capabilities, image compression is a great interest field of
research. Therefore, there is a strong demand towards the
efficient compression systems. The lossy and lossless
compressions are the two classes of the image compressions.
Lossless compression completely recovers the original data
when decompressing the compressed data. On the contrary,
lossy compression loses some information over the
compression-decompression process. Human eyes can’t
recognize small differences in two similar pictures. Thus,
Images can be compressed using lossy compression.
THE COMPUTATION COMPLEXITY
From the computation complexity point of view, the
proposed block-pruned 4x4 DTT algorithm is compared with
recent algorithms [17], [18], [19], and the traditional
separability-symmetry algorithm. We have to mention that
the scaled algorithm in [18] is considered here as a
normalized full version that require 16 multiplications as a
last stage to get the final output. Table I gives comparative
results of the compared algorithms with the proposed one in
terms of the number of multiplications, additions, and shifts
operations. Different block-pruned sizes out of 4x4 are
considered for our proposed algorithm complexity.
CONCLUSION
In this paper, a new fast algorithm of 2-D 4x4 DTT has
been proposed which is suitable for pruning in a block
fashion. Our proposed algorithm requires less computation
complexity in comparison with the recent published
algorithms. The basic idea behind the algorithm is to utilize
the symmetry property beside the distributed-arithmetic to
combine similar terms in linear combinations for each pruned
output. The block-pruned 4x4 DTT is used to reconstruct a
set of standard images showing that the DTT compression is
very similar to the DCT compression for the natural
photograph images. For the artificial images which have high
illumination variations, the DTT has higher energy
compactness than the DCT. For Future work, the
zigzag-order pruning of the 2-D DTT algorithm is an
interested research area as the zigzag scanning is more
suitable for image compression standard. As well as, the
regularity of the DTT algorithm is highly required.