&lt;title&gt;Fast scaled-DCT algorithm&lt;/title&gt;

Feig, Ephraim

doi:10.1117/12.19490

Cited by 49 publications

(25 citation statements)

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“…Their applications include image and video compression, [40]. Important algorithms for the trigonometric transforms were developed by Chen, Smith and Fralick [7], Wang [52], Yip and Rao [56,57], Vetterli and Nussbaumer [50], Lee [28], Feig [20], Chan and Ho [6], Steidl and Tasche [46], and Feig and Winograd [21].…”

Section: Transforms and Algorithmsmentioning

confidence: 99%

The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

Püschel¹,

Moura²

2003

SIAM J. Comput.

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Abstract. It is known that the discrete Fourier transform (DFT) used in digital signal processing can be characterized in the framework of representation theory of algebras, namely as the decomposition matrix for the regular module C[Zn] = C[x]/(x n − 1). This characterization provides deep insight on the DFT and can be used to derive and understand the structure of its fast algorithms. In this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated to four series of Chebyshev polynomials. Then we derive most of their known algorithms by pure algebraic means. We identify the mathematical principle behind each algorithm and give insight into its structure. Our results show that the connection between algebra and digital signal processing is stronger than previously understood.

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Section: Transforms and Algorithmsmentioning

confidence: 99%

The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

Püschel¹,

Moura²

2003

SIAM J. Comput.

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“…However, the implementation of the DCT is less expensive than that of the DWT. The most efficient algorithm for 2-D 8X8 DCT requires only 54 multiplications [11], while the complexity of calculating the DWT depends on the length of wavelet filters.…”

Section: A Image Compression Methods -Modifications or Replacement Omentioning

confidence: 99%

A Review On Segmentation Based I mage Compression Techniques

Thayammal¹,

Selvathi²

2013

JESTR

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-The storage and transmission of imagery become more challenging task in the current scenario of multimedia applications. Hence, an efficient compression scheme is highly essential for imagery, which reduces the requirement of storage medium and transmission bandwidth. Not only improvement in performance and also the compression techniques must converge quickly in order to apply them for real time applications. There are various algorithms have been done in image compression, but everyone has its own pros and cons. Here, an extensive analysis between existing methods is performed. Also, the use of existing works is highlighted, for developing the novel techniques which face the challenging task of image storage and transmission in multimedia applications.

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“…It is well acknowledged that hardware (or software) implementation of the DCT is less expensive than that of the wavelet transform. For example, the most efficient algorithm for the two-dimensional (2-D) 8 8 DCT requires only 54 multiplications [12], while the complexity of calculating the discrete wavelet transform depends on the length of the wavelet filters, which is at least one multiplication per coefficient. We hence focus on the performance comparison of DCT-and wavelet-based coders in this paper.…”

Section: Introductionmentioning

confidence: 99%

A comparative study of DCT- and wavelet-based image coding

Xiong

Ramchandran

Orchard

et al. 1999

IEEE Trans. Circuits Syst. Video Technol.

180

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Abstract-We undertake a study of the performance difference of the discrete cosine transform (DCT) and the wavelet transform for both image and video coding, while comparing other aspects of the coding system on an equal footing based on the state-of-theart coding techniques. Our studies reveal that, for still images, the wavelet transform outperforms the DCT typically by the order of about 1 dB in peak signal-to-noise ratio. For video coding, the advantage of wavelet schemes is less obvious. We believe that the image and video compression algorithm should be addressed from the overall system viewpoint: quantization, entropy coding, and the complex interplay among elements of the coding system are more important than spending all the efforts on optimizing the transform.Index Terms-Discrete cosine transform (DCT), image coding, video coding, wavelet transform.

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<title>Fast scaled-DCT algorithm</title>

Cited by 49 publications

References 0 publications

The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

A Review On Segmentation Based I mage Compression Techniques

A comparative study of DCT- and wavelet-based image coding

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