KR100677077B1 - Method for approximating fast discrete cosine transform - Google Patents

Abstract

The present invention relates to a Discrete Cosine Transform (DCT) method, and more particularly, to a fast discrete cosine transform approximation method for approximating the Lee algorithm to reduce the DCT calculation amount.

A fast discrete cosine transform approximation method according to the present invention is a fast cosine transform for calculating odd cosine and even terms separately in a discrete cosine transform (DCT) equation, wherein (a) the DCT arithmetic equation A method for approximating a cosine term, and (b) applying the approximated value to the Lee DCT algorithm to calculate a predetermined low frequency coefficient.

As a result, hardware reduction and operation time can be shortened.

Description

Method for approximating fast discrete cosine transform

1 is a DCT flow graph according to a Chen approximation DCT algorithm according to the related art.

2 is a DCT block configuration diagram for describing 2-D DCT.

3 is a DCT flow graph to which the fast discrete cosine transform approximation method according to the present invention is applied.

4 is a DCT flow graph by Lee DCT algorithm applied to the present invention.

The present invention relates to a Discrete Cosine Transform (DCT) method, and more particularly, to a fast discrete cosine transform approximation method for approximating the Lee algorithm to reduce the DCT calculation amount.

Conversion of 2D image information means conversion of data in a spatial domain to a frequency domain, which enables data compression by reducing correlation between coefficients. The orthogonal transformation, which removes the correlation, has the property of concentrating the maximum energy to the smallest possible coefficients.

One such orthogonal transform is DCT. And, the one-dimensional standard 8-point DCT equation is the same as Equation 1.

Applying Chen DCT, which is not approximated by Equation 1, has a large number of operations, especially multiplication operations, which greatly affects the overall performance of the system.

Accordingly, in order to reduce the number of operations, a scheme of approximating Equation 1 by the Chen DCT method is devised as follows.

cos (pi / 16), cos (3pi / 16) → cos (2pi / 16)

cos (5pi / 16), cos (7pi / 16) → cos (6pi / 16)

, ....

Applying the above approximation to Equation 1 is expressed as Equation 2.

는 최대 정수 ≤ x 이다.From here,

Is a maximum integer ≤ x.

The above approximation enables DCT butterfly coefficient approximation, which is shown in FIG. 1 as a DCT flow graph.

 Although the number of operations is reduced through this approximation, there are still problems that burden the system due to the excessive number of DCT operations because the addition operation must be performed 12 times and the multiplication operation 6 times.

SUMMARY OF THE INVENTION The present invention provides a fast discrete cosine transform approximation method for reducing the number of DCT operations by applying the Chen DCT approximation algorithm to the Lee DCT algorithm and performing scaling for integer operations to solve the above problems. have.

In order to achieve the above technical problem, the fast discrete cosine transform approximation method according to the present invention is a fast cosine transform for calculating odd cosine and even terms separately in a discrete cosine transform (DCT) equation. (a) in the DCT equation, comprising: approximating a cosine term; and (b) applying the approximated value to the Lee DCT algorithm to calculate a predetermined low frequency coefficient.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

First, the Lee DCT algorithm is as follows.

A general DCT equation is shown in Equation 3.

u = 0, 1, ..., N-1

, if u=0Where c (u) =

, if u = 0

               = 1, other than

e _2N ^{(2m + 1) u} = cos [(2m + 1) uπ / 2N], X '(u) = c (u) X (u)

The coefficient of u is divided into odd and even terms as follows.

x (m) = g (m) + h '(m)'

x (N-1-m) = g (m) -h '(m)

In Equation 4,5

e_2N ^(2m+1)u g (m) =

e _2N ^{(2m + 1) u}

e_2N ^(2m+1)(2u+1) h '(m) =

e _2N ^{(2m + 1) (2u + 1)}

to be.

And e _2N ^{(2m + 1) 2u} = e _N ^{(2m + 1) u} = e _{2 (N / 2)} ^{(2m + 1) u}

If X '(2u-1) │ _{u = 0} = 0, IDCT operation is as follows.

x (m) = g (m) + (1 / (2e2N (2m + 1))) h (k)

x (N-1-m) = g (m)-(1 / (2e2N (2m + 1))) h (k)

Where k = 0, 1, ..., (N / 2) -1.

The 8-point Lee DCT flow graph is displayed using the results as shown in FIG. 4.

항을 ,

(여기서

는 최대 정수 ≤ x) 항으로 변환시켜 근사화시키고, 일 예로 8 포인트 DCT 연산에서 저주파 계수를 4차 계수항까지만 연산시키는 DCT 플로우 그래프로 표시하면 도 3과 같다.In this Lee DCT algorithm operation,

Terms,

(here

3 is approximated by converting to a maximum integer ≤ x) term, and is represented as a DCT flow graph that calculates low frequency coefficients up to 4th order coefficient terms in an 8-point DCT operation as shown in FIG. 3.

Accordingly, four multiplication operations and 13 addition operations are required.

In addition, a one-dimensional DCT is performed by a four-point DCT by an eight-point DCT coefficient approximation, and as shown in FIG. Naturally, it can be applied.

Table 1 summarizes the DCT computation amount by the Chen approximation DCT algorithm according to the prior art and the DCT computation amount by the Lee approximation DCT algorithm according to the present invention.

Comparision of Chen and Lee DCTs Using Approximation Chen Lee 8 points DCT Multiplication count 16 12 Addition count 26 29 lower freg. coeff.4 DCT Multiplication count 6 4 Addition count 12 13

As shown in Table 1, the present invention shows that the multiplication operation is reduced twice and the addition is increased once when the low frequency coefficient is considered only up to the fourth order, compared to the conventional method of Chen DCT approximation. . In addition, in the case of calculating all coefficients, it can be seen that the multiplication operation amount is decreased four times and the addition operation is increased three times in comparison with the conventional technology in the eight-point DCT. In the operation, since multiplication requires a relatively large amount of computation compared to addition, although the addition operation is increased, it can be seen that the multiplication operation is reduced two or more times, thereby reducing the overall operation amount.

In the actual code, the multiplication operation is reduced twice because (1/2) cos (π / 4) multiplied in the 3rd step in the Lee algorithm is not multiplied. do. The amount of DCT calculation for this is summarized in Table 2.

Comparison of DCT Computations with Approximation and Scaling Chen Lee 8-point 1-D DCT Multiplication count 14 10 Addition count 26 29 4 lower freq. coeff (1-D) Multiplication count 4 2 Addition count 12 13 8 × 8 (1block) 2-D DCT Multiplication count 896 640 Addition count 1664 1856 4 × 4 (1 block) 2-D DCT (using lower freq. Coeff) Multiplication count 64 32 Addition count 192 208

Therefore, even when both approximation and scaling are considered, it can be seen that the present invention reduces the computation amount compared to the conventional Chen algorithm.

As described above, according to the present invention, by applying the DCT approximation algorithm to the Lee DCT algorithm to reduce the number of multiplication operations, there is an effect that can reduce hardware and shorten the computation time.

Claims (4)

In the Lee DCT algorithm approximation method, which is a fast cosine transform that separates odd and even terms from a discrete cosine transform (DCT) equation used for processing a video signal, respectively, (a) approximating a cosine term in the DCT equation; And and (b) applying the approximated value to the Lee DCT algorithm to compute a predetermined low frequency coefficient. The method of claim 1, wherein the discrete cosine transform (DCT) formula F (u)

u = 0, 1, ..., N-1 Where C (u) =

, if u = 0             = 1, other than And the approximation method in step (a) is

Term

, (here,

Fast integer cosine transform approximation method, characterized in that for converting the maximum integer ≤ x) term. delete The compound of claim 2, wherein C (u) =

A method for approximating a discrete cosine transform, characterized in that it is calculated by converting to a predetermined value and converting the result into an integer value.

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