Method and apparatus for restoring compressed image processing system and method of decoding a current image

Abstract

The present invention relates to an image processing technique, and in particular to a method for restoring a compressed image by using a hybrid motion compensation discrete cosine transform (hybrid MC/DCT) mechanism, including: a step of defining a smoothing functional having a smoothing degree of an image and reliability for an original image by pixels having an identical property in image block units; and a step of computing a restored image by performing a gradient operation on the smoothing functional in regard to the original image, thereby preventing the blocking artifacts and the ringing effects in regard to the pixels having an identical property in image blocks.

Description

Here, “g” and “f” indicate row vectors re-arranged in a stack-order, namely a scanning order, and “n” indicates a quantization error. When it is presumed that a size of the image is M×M, the original image (f), the reconstructed image (g) and (n) are column vectors having a size of M×1.

An original pixel for the original image (f) is represented by f(i,j). Here, “i” and “j” indicate a position of the pixel in the image.

FIG. 4 illustrates configuration of the original pixels f(i,j) in the block of the original image (f) in order to explain the present invention. Reference numerals in FIG. 4 depict information of the respective pixels. 8×8 pixels are shown in a single block.

The 8×8 pixels in the block are classified into the pixels having an identical property. That is, the pixels are divided in accordance with their position, vertical direction, horizontal direction and smoothing variation in the temporal section. Accordingly, it is defined that a set of the pixels positioned at a boundary of the block in a vertical direction is C_VB, a set of the pixels positioned inside the block in the vertical direction is C_VW, a set of the pixels positioned at a boundary of a block in a horizontal direction is C_HB, a set of the pixels positioned inside the block in the horizontal direction is C_HW, and a set of the pixels moved and compensated in the temporal section is C_T. The sets C_VB, C_VW, C_HB, C_HW, C_T are represented by the following expressions.
C_VB={f(i,j): i mod 8=0,1, and j=0,1, . . . , M−1}
C_VW={f(i,f): i mod 8≠0,1, and j=0,1, . . . , M−1}  (2)
C_HB={f(i,j): j mod 8=0,1, and i=0,1, . . . , M−1}
C_HW={f(i,j): j mod 8≠0,1, and i=0,1, . . . , M−1}
C_T={f(i,j): f(i,j)εMB_inter or f(i,j)εMB_{not coded}}

Here, the set C_T is a set of the pixels having a macro block type of “inter” or “not coded” in order to remove temporal redundancy information.

The smoothing functional M(f) for using the regularization restoration method from the above-defined sets C_VB, C_VW, C_HB, C_HW, C_T is defined as follows.
M(f)=M_VB(f)+M_HB(f)+M_VW(f)+M_HW(f)+M_T(f)   (3)

Here, M_VB(f) is a smoothing functional for the set C_VB, M_HB(f) is a smoothing functional for C_HB, M_VW(f) is a smoothing functional for the set C_VW, M_HW(f) is a smoothing functional for the set C_HW, and M_T(f) is a smoothing functional for the set C_T. The smoothing fuctionals are respectively defined as follows. $\begin{array}{c}{M}_{\mathrm{VB}}\left(f\right)=\parallel Q_{\mathrm{VB}}f{\parallel }^2+{\alpha }_{\mathrm{VB}}\parallel g-f{\parallel }_{W1}^2\\ M_{\mathrm{HB}}\left(f\right)=\parallel Q_{\mathrm{HB}}f{\parallel }^2+{\alpha }_{\mathrm{HB}}\parallel g-f{\parallel }_{W2}^2\\ M_{\mathrm{VW}}\left(f\right)=\parallel Q_{\mathrm{VW}}f{\parallel }^2+{\alpha }_{\mathrm{VW}}\parallel g-f{\parallel }_{W3}^2\\ M_{\mathrm{HW}}\left(f\right)=\parallel Q_{\mathrm{HW}}f{\parallel }^2+{\alpha }_{\mathrm{HW}}\parallel g-f{\parallel }_{W4}^2\\ M_T\left(f\right)=\parallel Q_{T}f{\parallel }^2+{\alpha }_T\parallel g-f{\parallel }_{W5}^2\end{array}$

Here, first terms in each expression indicate a smoothing degree for the original pixel (reference pixel) and adjacent pixel, and second terms indicate reliability for the original pixel and the restored pixel. “∥.∥” indicates the Euclidean norm. Q_VB, Q_VW, Q_HB, Q_HW, Q_T indicate high pass filters for smoothing the pixels in the sets C_VB, C_VW, C_HB, C_HW, C_T.

The first term at the right side is represented by the following expression. $\begin{array}{cc}\begin{array}{c}\parallel Q_{\mathrm{VB}}f{\parallel }^2=\sum _{n=0}^{M-1}\sum _m{\left(f\left(m,n\right)-f\left(m-1,n\right)\right)}^2,m=0,8,16,\dots \\ \parallel Q_{\mathrm{HB}}f{\parallel }^2=\sum _n\sum _{n=0}^{M-1}{\left(f\left(m,n\right)-f\left(m,n-1\right)\right)}^2,n=0,8,16,\dots \\ \parallel Q_{\mathrm{VW}}f{\parallel }^2=\sum _{n=0}^{M-1}\sum _m{\left(f\left(m,n\right)-f\left(m-1,n\right)\right)}^2,m\ne 0,8,16,\dots \\ \parallel Q_{\mathrm{HW}}f{\parallel }^2=\sum _n\sum _{n=0}^{M-1}{\left(f\left(m,n\right)-f\left(m,n-1\right)\right)}^2,n\ne 0,8,16,\dots \\ \parallel Q_{T}f{\parallel }^2=\sum _n\sum _m{\left(f_{\mathrm{MC}}\left(m,n\right)-f\left(m,n\right)\right)}^2\end{array}& \left(5\right)\end{array}$

The smoothing functionals represented by Expression (4) are quadratic equations, respectively. Thus, local minimizers of each smoothing functional become global minimizers.

FIG. 5 illustrates directions of the irregular smoothing degree of the pixels. There are a single pixel at the center and eight pixels therearound. There are also shown horizontal and vertical arrows starting from the pixel at the center. The arrows respectively depict the directions of the irregular smoothing degree in regard to the four adjacent pixels. That is to say, the irregular smoothing degree is considered in four directions in respect of a single pixel.

FIG. 6 illustrates an image moved and compensated in regard to the temporal section in accordance with the present invention. Arrows depict the correlation of a currently-restored image with a previously-restored image and a succeedingly reconstructed image, respectively.

α_VB, α_HB, α_VW, α_HW, α_T included in the second terms of Expression (4) are regularization parameters in regard to each set, indicate a ratio of the smoothing degree and reliability, and imply an error element. W1, W2, W3, W4, W5 indicate diagonal matrixes having a size of M×M in order to determine whether each set has an element, and have a value of “1”, or “0” according to whether each pixel is included in a corresponding set. That is, if the respective pixels are included in the corresponding sets, the value of the diagonal elements is “0”. If not, the value of the diagonal elements is

Thereafter, the regularization parameters, α_VB, α_HB, α_VW, α_HW, α_T are approximated as follows.

Approximation of Regularization Parameters

Approximation of the regularization parameters is a major element determining performance of the smoothing functional. In order to reduce the computation amount, presumptions are made as follows.

• (1) A maximum value of the quantization error generated in the quantization process of the DCT region is Qp, and thus it is presumed that the quantization variables Qp are regular in each macro block. For this, the maximum quantization error of the DCT coefficients of each macro block is regularly set to be Qp.
• (2) It is also presumed that the DCT quantization errors have the Gaussian distribution property in the spatial section.

Under the above presumptions, in case a set theoretic is applied, each regularization parameter is approximated as follows. $\begin{array}{cc}\begin{array}{c}{\alpha }_{\mathrm{VB}}=\frac{\parallel Q_{\mathrm{VB}}f{\parallel }^2}{\parallel g-f{\parallel }_{W1}^2}=\frac{\parallel Q_{\mathrm{VB}}g{\parallel }^2}{\parallel g-f{\parallel }_{W1}^2}=\frac{\parallel Q_{\mathrm{VB}}g{\parallel }^2}{\sum _n\sum _m{w}_1\left(m,n\right){\mathrm{Qp}}^2\left(m,n\right)}\\ {\alpha }_{\mathrm{HB}}=\frac{\parallel Q_{\mathrm{HB}}f{\parallel }^2}{\parallel g-f{\parallel }_{W2}^2}=\frac{\parallel Q_{\mathrm{HB}}g{\parallel }^2}{\parallel g-f{\parallel }_{W2}^2}=\frac{\parallel Q_{\mathrm{HB}}g{\parallel }^2}{\sum _n\sum _m{w}_2\left(m,n\right){\mathrm{Qp}}^2\left(m,n\right)}\\ {\alpha }_{\mathrm{VW}}=\frac{\parallel Q_{\mathrm{VW}}f{\parallel }^2}{\parallel g-f{\parallel }_{W3}^2}=\frac{\parallel Q_{\mathrm{VW}}g{\parallel }^2}{\parallel g-f{\parallel }_{W3}^2}=\frac{\parallel Q_{\mathrm{VW}}g{\parallel }^2}{\sum _n\sum _m{w}_3\left(m,n\right){\mathrm{Qp}}^2\left(m,n\right)}\\ {\alpha }_{\mathrm{HW}}=\frac{\parallel Q_{\mathrm{HW}}f{\parallel }^2}{\parallel g-f{\parallel }_{W4}^2}=\frac{\parallel Q_{\mathrm{HW}}g{\parallel }^2}{\parallel g-f{\parallel }_{W4}^2}=\frac{\parallel Q_{\mathrm{HW}}g{\parallel }^2}{\sum _n\sum _m{w}_4\left(m,n\right){\mathrm{Qp}}^2\left(m,n\right)}\\ {\alpha }_T=\frac{\parallel Q_{T}f{\parallel }^2}{\parallel g-f{\parallel }_{W5}^2}=\frac{\parallel Q_{T}g{\parallel }^2}{\parallel g-f{\parallel }_{W5}^2}=\frac{\parallel Q_{T}g{\parallel }^2}{\sum _n\sum _m{w}_5\left(m,n\right){\mathrm{Qp}}^2\left(m,n\right)}\end{array}& \left(6\right)\end{array}$

Here, Q²_p(m,n) is a quantization variable of a macro block including a (m,n)th pixel of a two-dimensional image.

In Expression (6), denominator terms of the respective regularization parameters are a sum of the energy for the quantization noise of the elements included in each group. As described above, the values of the regularization parameters may be easily computed by applying the set theoretic under the two presumptions.

Computing Pixels to be Restored From Smoothing Functional

Only the original image needs to be computed. However, the smoothing functional includes a square term of the original image. Accordingly, in order to compute the original image, a gradient operation is carried out on the smoothing functional in regard to the original image. A result value thereof is “0”, and represented by the following expression.
∇_fM(f)=2Q^T_VBQ_VB+2Q^T_HBQ_HB+
2Q^T_VW
Q_VW+2Q^T_HWQ_HW+2Q^T
TQ_T−2α_VBW^T₁W₁(
g−f)−2α_HBW^T₂W₂(
g−f)−2α_VWW^T₃W₃(
g−f)−2α_HWW^T₄W₄(
g−f)−2α_T(g−f)=0   (7)

Here, a superscript “T” indicates a transposition of the matrix.

A restored image similar to the original image (f) can be obtained by Expression (7). However, operation of an inverse matrix must be performed, and thus the computation amount is increased. Thus, in accordance with the present invention, the restored image is computed by an iterative technique which will now be explained.

Iterative Technique

When Expression (7) is iterated k times, an iterative solution f_k+1 is represented by the following expression.
f_k+1=f_k+β[Ag−Bf_k],
A=α_VBW₁+α_HBW₂+α_VWW₃+α_HWW₄+α_TW₅   (8)
B=(Q^T_VBQ_VB+Q^T_HBQ_HB+Q^T_VWQ_VW+Q^T_HWQ_HW+Q^T_TQ_T)+A

In Expression (8), “β” is a relaxation parameter having a convergence property. Expression (8) can be represented by the following expression by computing consecutive iterative solutions.
(f_k+1−f_K)=(I−B)(f_k−f_k−1)   (9)

Here, “I” is an identity matrix, and the matrix B has a positive definite property. Therefore, when the following condition is satisfied, the iterative solutions are converged.
∥I−B∥<1   (10)

Expression (10) can be summarized as follows. $\begin{array}{cc}0<\beta <\frac{2}{1={\max }_i{\lambda }_i\left(A\right)}& \left(11\right)\end{array}$

In Expression (11), “λ(A)” depicts an eigen value of the matrix A. A considerable amount of computation is required to compute the eigen value λ(A). However, the high pass filters have a certain shape determined according to the positions of the respective pixels, regardless of the image. Accordingly, before computing Expression (8), the eigen value λ(A) can be replaced by a fixed value. The value may be computed by a power method which has been generally used in interpretation of numerical values.

For example, a computation process of an eigen value of an iterative solution will now be explained.
x_k+1=Kx_k
Here, “x_k” is a vector of M×1, and “K” is a positive-definite symmetric M×M matrix. The eigen value λ′ of the matrix K is approximated as follows. ${\lambda }^{\prime }=\frac{{\left(x_{k+1}\right)}^T{x}_k}{\left(x_k^T\right)x_k}$

In the above expression, if “k” is to infinity, the eigen value λ′ is approximated to a real value.

Thus, the iterative solution represented by Expression (8) is computed. The next thing to be considered is a time of finishing the iterative technique, in order to determine the number of iteration. Here, two standards are set as follows.

Firstly, a predetermined threshold value is set before starting iteration, an image obtained after iteration, namely a partially-restored image is compared with the previously-set threshold value, and it is determined whether the iteration technique is continuously performed according to a comparison result.

Secondly, the iteration technique is performed as many as a predetermined number, and then finished.

According to the first standard, a predetermined threshold value is set in performing iteration, and thus a wanted value is obtained. However, although the iteration number is increased, it may happen that the predetermined threshold value is not reached. On the other hand, the second standard is performed by experience, but can reduce a computation amount. Therefore, the two standards may be selectively used according to the design specification.

FIG. 7 is a flowchart of the apparatus for restoring the compressed image of the image processing system in accordance with the present invention. As shown therein, in the step S1, the quantization variable Qp and the image signals Y, U, V are inputted, and the regularization parameter is approximated as described above. In the step S2, the gradient operation is performed on the smoothing functional in regard to the original image. In the step S3, an iterative solution, namely a wanted restored image is obtained by the iteration technique. In this step, employed are the image signals Y, U, V and the motion vector MV which is moved and compensated.

In the step S4, the DCT is performed on the restored image corresponding to the iterative solution f_k+1 obtained in the step S3. An (u,v)th DCT coefficient of the two-dimensional restored image is expressed as F_k+1(u,v), and must exist in the following section in accordance with a property of the quantization process.
G(u,v)−Qp≦F_k+1(u,v)≦G(u,v)+Qp   (12)

Here, “Qp” is a maximum quantization error as explained above, and “G(u,v)” is a two-dimensional DCT coefficient obtained by performing the DCT on the reconstructed image (g). The DCT coefficients F_k+1(u,v) and G(u,v) are represented as follows. In Expression (13), “B” indicates a block DCT.
F_k+1(u,v)=(Bf_k+1)(u,v), and G(u,v)=(Bg)(u,v)   (13)

In the step S6, a section of the DCT coefficient of the restored image is set as in Expression (12). Accordingly, in case the DCT coefficient F_k+1(u,v) of the restored image is not in the predetermined section, it must be projected as follows. A projection process is carried out in the step S7, and represented by Expression (14).
P(F_k+1(u,v))=G(u,v)−Qp, if F_k+1(u,v)<G(u,v)−Qp
P(F_k+1(u,v))=G(u,v)+Qp, if F_k+1(u,v)>G(u,v)−Qp   14
P(F_k+1(u,v))=F_k+1(u,v), otherwise.

Expression (14) will now be described.

When F_k+1(u,v) is smaller than G(u,v)−Qp, the projected restored image P(F_k+1(u,v)) is mapped to G(u,v)−Qp. In case F_k+1(u,v) is greater than G(u,v)+Qp, the projected restored image P(F_k+1(u,v)) is mapped to G(u,v)+Qp. Otherwise, the projected restored image P(F_k+1(u,v)) is mapped as it is.

In the step S8, the inverse DCT is performed on the mapped image P(F_k+1(u,v)) in the spatial section. The finally restored image is represented by Expression (14).
f_k+1=B^TPBf_k+1   (15)

Here, “B” indicates the DCT, “P” indicates mapping, and “B^T” indicates the inverse DCT.

The restored image is stored in a frame memory in the post processing unit 220 (Step S9). The post processing unit 220 performs motion compensation based on the motion vector MV (Step S10). The motion and compensation image is employed for generation of the regularization parameter for a succeeding image and the iteration technique.

The post processing unit 220 outputs the restored motion and compensation image as a video signal to a display (not shown) (Step S11).

As discussed earlier, the present invention can restrict a section of the restored image for the respective pixels by using the various regularization parameters. In addition, the present invention prevents flickering which may occur in the dynamic image compression technique.

Consequently, the present invention adaptively prevents the blocking artifacts and the ringing effects for the pixels having an identical property in image block units, and thus can be widely used for the products of the hybrid MC-DCT mechanism.

As the present invention may be embodied in several forms without departing from the spirit or essential characteristics thereof, it should also be understood that the above-described embodiment is not limited by any of the details of the foregoing description, unless otherwise specified, but rather should be construed broadly within its spirit and scope as defined in the appended claims, and therefore all changes and modifications that fall within the meets and bounds of the claims, or equivalences of such meets and bounds are therefore intended to be embraced by the appended claims.

Claims

1. A method for restoring a compressed image of an image processing system, comprising:

a step for defining a smoothing functional having a smoothing degree of an image and reliability for an original image by pixels having an identical property in image block units; and

a step for computing a restored image by performing a gradient operation on the smoothing functional in regard to the original image;

wherein the smoothing functional m(f) comprises a sum of a smoothing functional m_VB(f) for pixels positioned at the boundary of a block in a vertical direction, a smoothing functional m_VW(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional m_HB(f) for pixels positioned at the boundary of a block in a horizontal direction, a smoothing functional m_HW(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional m_T(f) for pixels moved and compensated in the temporal section, “f” indicating the original image.

2. The method according to claim 1, wherein the step for defining the smoothing functional divides the pixels according to their position, horizontal direction, vertical direction and smoothing variation in a temporal section.

3. The method according to claim 1, wherein the smoothing functionals m_VB(f), m_HB(f), m_VW(f), m_HW(f), m_T(f) are defined as; $\begin{array}{c}{\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{VB}}\left(f\right)=\parallel Q_{\mathrm{VB}}f{\parallel }^2+{\alpha }_{\mathrm{VB}}\parallel g-f{\parallel }_{W1}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{HB}}\left(f\right)=\parallel Q_{\mathrm{HB}}f{\parallel }^2+{\alpha }_{\mathrm{HB}}\parallel g-f{\parallel }_{W2}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{VW}}\left(f\right)=\parallel Q_{\mathrm{VW}}f{\parallel }^2+{\alpha }_{\mathrm{VW}}\parallel g-f{\parallel }_{W3}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{HW}}\left(f\right)=\parallel Q_{\mathrm{HW}}f{\parallel }^2+{\alpha }_{\mathrm{HW}}\parallel g-f{\parallel }_{W4}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_T\left(f\right)=\parallel Q_{T}f{\parallel }^2+{\alpha }_T\parallel g-f{\parallel }_{W5}^2\end{array}$

Q_VB, Q_VW, Q_HB, Q_HW, Q_T indicating high pass filters for smoothing the respective pixels, α_VB, α_VW, α_HB, α_HW, α_T being regularization parameters, g being a reconstructed image, and W1, W2, W3, W4, W5 indicating diagonal matrixes for determining whether each group has an element.

4. The method according to claim 1, wherein the step for computing the restored image comprises a step for approximating the regularization parameter by applying a set theoretic, and it is presumed that the quantization variables of the DCT region regular in each macro block, and also presumed that the DCT quantization errors have the Gaussian distribution property in the spatial section.

5. The method according to claim 4, wherein the regularization parameters are approximated as; $\begin{array}{c}{\alpha }_{\mathrm{VB}}=\frac{\parallel Q_{\mathrm{VB}}f{\parallel }^2}{\parallel g-f{\parallel }_{W1}^2}=\frac{\parallel Q_{\mathrm{VB}}g{\parallel }^2}{\parallel g-f{\parallel }_{W1}^2}=\frac{\parallel Q_{\mathrm{VB}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{w}_1\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_{\mathrm{HB}}=\frac{\parallel Q_{\mathrm{HB}}f{\parallel }^2}{\parallel g-f{\parallel }_{W2}^2}=\frac{\parallel Q_{\mathrm{HB}}g{\parallel }^2}{\parallel g-f{\parallel }_{W2}^2}=\frac{\parallel Q_{\mathrm{HB}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{w}_2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_{\mathrm{VW}}=\frac{\parallel Q_{\mathrm{VW}}f{\parallel }^2}{\parallel g-f{\parallel }_{W3}^2}=\frac{\parallel Q_{\mathrm{VW}}g{\parallel }^2}{\parallel g-f{\parallel }_{W3}^2}=\frac{\parallel Q_{\mathrm{VW}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{w}_3\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_{\mathrm{HW}}=\frac{\parallel Q_{\mathrm{HW}}f{\parallel }^2}{\parallel g-f{\parallel }_{W4}^2}=\frac{\parallel Q_{\mathrm{HW}}g{\parallel }^2}{\parallel g-f{\parallel }_{W4}^2}=\frac{\parallel Q_{\mathrm{HW}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{w}_4\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_T=\frac{\parallel Q_{T}f{\parallel }^2}{\parallel g-f{\parallel }_{W5}^2}=\frac{\parallel Q_{T}g{\parallel }^2}{\parallel g-f{\parallel }_{W5}^2}=\frac{\parallel Q_{T}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{w}_5\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\end{array}$

Q²_p(m,n) indicating a quantization variable of a macro block including an (m,n)th pixel of a two-dimensional image.

6. The method according to claim 1, wherein a local minimizer of the smoothing functional is a global minimizer.

7. The method according to claim 1, wherein the regularization parameter indicates a ratio of a smoothing degree of the image and reliability for the original image.

8. The method according to claim 1, further comprising a step for computing an iterative solution in regard to a restored image, after computing the restored image.

9. The method according to claim 8, wherein the iterative solution f_k+1 is represented by;

f_k+1=f_k+β[Ag−Bf_k],

A=α_VBW₁+α_HBW₂+α_VWW₃+α_HWW₄+α_TW₅

B=(Q^T_VBQ_VB+Q^T_HBQ_HB+Q^T_VWQ_VW+Q^T_HWQ_HW+Q^T_TQ_T)+A

and, β is a relaxation parameter having a convergence property, and computed at the range of $0<\beta <\frac{2}{1={\max }_i{\lambda }_i\left(A\right)},$

 an eigen value λ(A) of the matrix A being replaced by a fixed value.

10. The method according to claim 8, wherein a predetermined threshold value is set in computing an iterative solution, an image obtained after iteration is compared with the previously-set threshold value, and it is determined whether the iteration technique is continuously performed according to a comparison result, or the iteration is finished after the iteration technique is performed as many as a previously-set number.

11. The method according to claim 8, further comprising a step for obtaining a mapped image by projecting a two-dimensional DCT coefficient of the restored image corresponding to a computed iterative solution, and for performing an inverse DCT on the mapped image.

12. The method according to claim 11, wherein the step for obtaining the mapped image is mapping a projected restored image P(F_k+1(u,v)) to G(u,v)−Qp when the DCT coefficient of the restored image F_k+1(u,v) is smaller than G(u,v)−Qp, mapping the projected restored image P(F_k+1(u, v)) to G(u,v)+Qp when F_k+1(u,v) is greater than G(u,v)+Qp, and otherwise mapping the projected restored image P(F_k+1(u,v)) as it is, G(u,v) indicating a two-dimensional DCT coefficient obtained by performing the DCT on the reconstructed image, and Qp indicating quantization information.

13. The method according to claim 1, wherein a predetermined threshold value is set in computing an iterative solution, an image obtained after iteration is compared with the previously-set threshold value, and it is determined whether the iteration technique is continuously performed according to a comparison result, or the iteration is finished after the iteration technique is performed as many as a previously-set number.

14. The method according to claim 1, further comprising a step for obtaining a mapped image by projecting a two-dimensional DCT coefficient of the restored image corresponding to a computed iterative solution, and for performing an inverse DCT on the mapped image.

15. The method according to claim 14, wherein the step for obtaining the mapped image is mapping a projected restored image P(F_k+1(u,v)) to G(u,v)−Qp when the DCT coefficient of the restored image F_k+1(u,v) is smaller than G(u,v)−Qp, mapping the projected restored image P(F_k+1(u, v)) to G(u,v)+Qp when F_k+1(u,v) is greater than G(u,v)+Qp, and otherwise mapping the projected restored image P(F_k+1(u,v)) as it is, G(u,v) indicating a two-dimensional DCT coefficient obtained by performing the DCT on the reconstructed image, and Qp indicating quantization information.

16. An apparatus for restoring a compressed image of an image processing system, comprising:

a decoder for decoding a coded image signal, and for outputting information of the restored image, such as the decoded image, a quantization variable, a macro block type and a motion vector; and

a post processing unit for including the information of the restored image inputted from the image decoder, for defining a smoothing functional including a sum of a smoothing functional m_VB(f) for pixels positioned at the boundary of a block in a vertical direction, a smoothing functional m_VW(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional m_HB(f) for pixels positioned at the boundary of a block in a horizontal direction, a smoothing functional m_HW(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional m_T(f) for pixels moved and compensated in the temporal section, “f” indicating the original image, and for performing a gradient operation on the smoothing functional in regard to the original image,

the smoothing functional including a regularization parameter having weight of reliability for the original image.

17. A method for restoring a compressed image of an image processing system, comprising:

a step for defining a smoothing functional having a smoothing degree of an image and reliability for an original image by pixels having an identical property in image blocks units;

a step for computing a restored image by performing a gradient operation on the smoothing functional in regard to the original image; and

a step for computing an iterative solution in regard to the restored image, after computing the restored image.

18. The method according to claim 17, wherein the step for defining the smoothing functional divided the pixels according to their position, horizontal direction, vertical direction and smoothing variation in a temporal section.

19. The method according to claim 17, wherein the smoothing functional m(f) comprises a sum of a smoothing functional m_VB(f) for pixels positioned at the boundary of a block in a vertical direction, a smoothing functional m_VW(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional m_HB(f) for pixels positioned at the boundary of a block in a horizontal direction, a smoothing functional m_HW(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional m_T(f) for pixels moved and compensated in the temporal section, “f” indicating the original image.

20. The method according to claim 19, wherein the smoothing functionals m_VB(f), m_HB(f), m_VW(f), m_HW(f), m_T(f) are defined as; $\begin{array}{c}{\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{VB}}\left(f\right)=\parallel Q_{\mathrm{VB}}f{\parallel }^2+{\alpha }_{\mathrm{VB}}\parallel g-f{\parallel }_{W1}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{HB}}\left(f\right)=\parallel Q_{\mathrm{HB}}f{\parallel }^2+{\alpha }_{\mathrm{HB}}\parallel g-f{\parallel }_{W2}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{VW}}\left(f\right)=\parallel Q_{\mathrm{VW}}f{\parallel }^2+{\alpha }_{\mathrm{VW}}\parallel g-f{\parallel }_{W3}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_{\mathrm{HW}}\left(f\right)=\parallel Q_{\mathrm{HW}}f{\parallel }^2+{\alpha }_{\mathrm{HW}}\parallel g-f{\parallel }_{W4}^2\\ {\mathrm{<span\; class="c7\; g0">m</span>}}_T\left(f\right)=\parallel Q_{T}f{\parallel }^2+{\alpha }_T\parallel g-f{\parallel }_{W5}^2\end{array}$

Q_VB, Q_VW, Q_HB, Q_HW, Q_T indicating high pass filters for smoothing the respective pixels, α_VB, α_VW, α_HB, α_HW, α_T being regularization parameters, g being a reconstructed image, and W1, W2, W3, W4, W5 indicating diagonal matrixes for determining whether each group has an element.

21. The method according to claim 17, wherein the step for computing the restored image comprises a step for approximately the regularization parameter by applying a set theoretic, and it is presumed that the quantization variables of the DCT region are regular in each macro block, and also presumed that the DCT quantization errors have the Gaussian distribution property in the spatial section.

22. The method according to claim 21, wherein the regularization parameters are approximated as; $\begin{array}{c}{\alpha }_{\mathrm{VB}}=\frac{\parallel Q_{\mathrm{VB}}f{\parallel }^2}{\parallel g-f{\parallel }_{W1}^2}=\frac{\parallel Q_{\mathrm{VB}}g{\parallel }^2}{\parallel g-f{\parallel }_{W1}^2}=\frac{\parallel Q_{\mathrm{VB}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{W}_1\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_{\mathrm{HB}}=\frac{\parallel Q_{\mathrm{HB}}f{\parallel }^2}{\parallel g-f{\parallel }_{W2}^2}=\frac{\parallel Q_{\mathrm{HB}}g{\parallel }^2}{\parallel g-f{\parallel }_{W2}^2}=\frac{\parallel Q_{\mathrm{HB}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{W}_2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_{\mathrm{VW}}=\frac{\parallel Q_{\mathrm{VW}}f{\parallel }^2}{\parallel g-f{\parallel }_{W3}^2}=\frac{\parallel Q_{\mathrm{VW}}g{\parallel }^2}{\parallel g-f{\parallel }_{W3}^2}=\frac{\parallel Q_{\mathrm{VW}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{W}_3\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_{\mathrm{HW}}=\frac{\parallel Q_{\mathrm{HW}}f{\parallel }^2}{\parallel g-f{\parallel }_{W4}^2}=\frac{\parallel Q_{\mathrm{HW}}g{\parallel }^2}{\parallel g-f{\parallel }_{W4}^2}=\frac{\parallel Q_{\mathrm{HW}}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{W}_4\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\\ {\alpha }_T=\frac{\parallel Q_{T}f{\parallel }^2}{\parallel g-f{\parallel }_{W5}^2}=\frac{\parallel Q_{T}g{\parallel }^2}{\parallel g-f{\parallel }_{W5}^2}=\frac{\parallel Q_{T}g{\parallel }^2}{\sum _n\sum _{\mathrm{<span\; class="c7\; g0">m</span>}}{W}_5\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right){\mathrm{Qp}}^2\left(\mathrm{<span\; class="c7\; g0">m</span>},n\right)}\end{array}$

Q²_p(m,n) indicating a quantization variable of a macro block including an (m,n)th pixel of a two-dimensional image.

23. The method according to claim 17, wherein a local minimizer of the smoothing functional is a global minimizer.

24. The method according to claim 17, wherein the regularization parameter indicates a ratio of a smoothing degree of the image and reliability for the original image.

25. The method according to claim 17, wherein the iterative solution f_k+1 is represented by;

f_k+1=f_k+β[Ag−Bf_k],

A=α_VBW₁+α_HBW₂+α_VWW₃+α_HWW₄+α_TW₅

B=(Q^T_VBQ_VB+Q^T_HBQ_HB+Q^T_VWQ_VW+Q^T_HWQ_HW+Q^T_TQ_T)+A

and, β is a relaxation parameter having a convergence property, and computed at the range of $0<\beta <\frac{2}{1={\max }_i{\lambda }_i\left(A\right)},$

 an eigen value λ(A) of the matrix A being replaced by a fixed value.

26. An apparatus for restoring a compressed image of an image processing system, comprising:

a decoder for decoding a coded image signal, and for outputting information of the restored image, such as the decoding image, a quantization variable, a macro block type and a motion vector; and

a post processing unit for including the information of the restored image inputted from the image decoder, for defining a smoothing functional including a smoothing degree of the image and reliability of an original image block unit, and for performing a gradient operation on the smoothing functional in regard to the original image,

the smoothing functional including a regularization parameter having weight of reliability for the original image.

27. A method of decoding a current image, comprising:

obtaining a pixel value for a subject pixel in a current block and a pixel value for at least one pixel adjacent to the subject pixel;

obtaining a difference between the obtained pixel value for the subject pixel and the obtained pixel value for the adjacent pixel;

determining a pixel value for a pixel in the current block based on a smoothing function corresponding to a set of pixels determined based on a position of the subject pixel, the smoothing function having a smoothing degree based on the obtained difference; wherein

the smoothing function includes one of a first sub-smoothing function for pixels positioned at a boundary of the current block in a vertical direction; a second sub-smoothing function for pixels positioned at a boundary of the current block in a horizontal direction; a third sub-smoothing function for pixels positioned inside the current block in the vertical direction; a fourth sub-smoothing function for pixels positioned inside the current block in the horizontal direction; and a fifth sub-smoothing function for temporally separated pixels.

28. The method of claim 27, wherein the smoothing function includes at least one term representing reliability of the determined pixel value with respect to an associated original pixel value.

29. The method of claim 27, wherein the determining step includes performing a gradient operation on the smoothing function.

30. The method of claim 27, wherein the set of pixels includes at least one of the pixels positioned at the boundary of the current block in the vertical direction, the pixels positioned at the boundary of the current block in the horizontal direction, the pixels positioned inside the current block in the vertical direction, the pixels positioned inside the current block in the horizontal direction, and the temporally separated pixels.

31. The method of claim 27, wherein at least one of the first, second, third, fourth and fifth sub-smoothing functions involves pixel values associated with one of an original image and the current image.

32. The method of claim 27, wherein the subject pixel and the adjacent pixel are in different blocks.

33. The method of claim 27, wherein the determined pixel value is a restored pixel value for the subject pixel.