12,104 research outputs found
Fast algorithm for the 3-D DCT-II
Recently, many applications for three-dimensional
(3-D) image and video compression have been proposed using 3-D discrete cosine transforms (3-D DCTs). Among different types of DCTs, the type-II DCT (DCT-II) is the most used. In order to use the 3-D DCTs in practical applications, fast 3-D algorithms are essential. Therefore, in this paper, the 3-D vector-radix decimation-in-frequency (3-D VR DIF) algorithm that calculates the 3-D DCT-II directly is introduced. The mathematical analysis and the implementation of the developed algorithm are presented,
showing that this algorithm possesses a regular structure, can be implemented in-place for efficient use of memory, and is faster than the conventional row-column-frame (RCF) approach. Furthermore, an application of 3-D video compression-based 3-D DCT-II is implemented using the 3-D new algorithm. This has led to a substantial speed improvement for 3-D DCT-II-based compression systems and proved the validity of the developed algorithm
Overview of Parallel Platforms for Common High Performance Computing
The paper deals with various parallel platforms used for high performance computing in the signal processing domain. More precisely, the methods exploiting the multicores central processing units such as message passing interface and OpenMP are taken into account. The properties of the programming methods are experimentally proved in the application of a fast Fourier transform and a discrete cosine transform and they are compared with the possibilities of MATLAB's built-in functions and Texas Instruments digital signal processors with very long instruction word architectures. New FFT and DCT implementations were proposed and tested. The implementation phase was compared with CPU based computing methods and with possibilities of the Texas Instruments digital signal processing library on C6747 floating-point DSPs. The optimal combination of computing methods in the signal processing domain and new, fast routines' implementation is proposed as well
On Polynomial Multiplication in Chebyshev Basis
In a recent paper Lima, Panario and Wang have provided a new method to
multiply polynomials in Chebyshev basis which aims at reducing the total number
of multiplication when polynomials have small degree. Their idea is to use
Karatsuba's multiplication scheme to improve upon the naive method but without
being able to get rid of its quadratic complexity. In this paper, we extend
their result by providing a reduction scheme which allows to multiply
polynomial in Chebyshev basis by using algorithms from the monomial basis case
and therefore get the same asymptotic complexity estimate. Our reduction allows
to use any of these algorithms without converting polynomials input to monomial
basis which therefore provide a more direct reduction scheme then the one using
conversions. We also demonstrate that our reduction is efficient in practice,
and even outperform the performance of the best known algorithm for Chebyshev
basis when polynomials have large degree. Finally, we demonstrate a linear time
equivalence between the polynomial multiplication problem under monomial basis
and under Chebyshev basis
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
We present algorithms for the discrete cosine transform (DCT) and discrete
sine transform (DST), of types II and III, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~ 2N log_2 N to ~ (17/9) N log_2 N for a power-of-two transform size N.
Furthermore, we show that a further N multiplications may be saved by a certain
rescaling of the inputs or outputs, generalizing a well-known technique for N=8
by Arai et al. These results are derived by considering the DCT to be a special
case of a DFT of length 4N, with certain symmetries, and then pruning redundant
operations from a recent improved fast Fourier transform algorithm (based on a
recursive rescaling of the conjugate-pair split radix algorithm). The improved
algorithms for DCT-III, DST-II, and DST-III follow immediately from the
improved count for the DCT-II.Comment: 9 page
Fast watermarking of MPEG-1/2 streams using compressed-domain perceptual embedding and a generalized correlator detector
A novel technique is proposed for watermarking of MPEG-1 and MPEG-2 compressed video streams. The proposed scheme is applied directly in the domain of MPEG-1 system streams and MPEG-2 program streams (multiplexed streams). Perceptual models are used during the embedding process in order to avoid degradation of the video quality. The watermark is detected without the use of the original video sequence. A modified correlation-based detector is introduced that applies nonlinear preprocessing before correlation. Experimental evaluation demonstrates that the proposed scheme is able to withstand several common attacks. The resulting watermarking system is very fast and therefore suitable for copyright protection of compressed video
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and
discrete sine transform (DST-IV), as well as for the modified discrete cosine
transform (MDCT) and its inverse, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact
count is strictly lowered for all N > 4. These results are derived by
considering the DCT to be a special case of a DFT of length 8N, with certain
symmetries, and then pruning redundant operations from a recent improved fast
Fourier transform algorithm (based on a recursive rescaling of the
conjugate-pair split radix algorithm). The improved algorithms for DST-IV and
MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page
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