Pulse or digital communications – Bandwidth reduction or expansion – Television or motion video signal
Reexamination Certificate
2000-05-02
2002-01-15
Britton, Howard (Department: 2613)
Pulse or digital communications
Bandwidth reduction or expansion
Television or motion video signal
Reexamination Certificate
active
06339615
ABSTRACT:
TECHNICAL FIELD
This invention relates to a picture encoding device, a picture encoding method, a picture decoding device, a picture decoding method, and a recording medium. Particularly, it relates to a picture encoding device, a picture encoding method, a picture decoding device, a picture decoding method, and a recording medium adapted for thinning and compression-coding a picture so that a decoded picture substantially equivalent to an original picture may be provided.
BACKGROUND ART
In the case where a picture of standard resolution or low resolution (hereinafter referred to as an SD picture) is to be converted to a picture of high resolution (hereinafter referred to as an HD picture) or in the case where a picture is to be enlarged, the pixel value of a lacked pixel is interpolated (compensated) by a so-called interpolation filter.
However, since a component (high-frequency component) of the HD picture which is not included in the SD picture cannot be restored even by carrying out interpolation of a pixel by the interpolation filter, it has been difficult to provide a picture of high resolution.
Thus, the present Assignee has proposed a picture converting device (picture converting circuit) for converting an SD picture to an HD picture which also includes a high-frequency component not included in the SD picture.
In this picture converting device, adaptive processing for finding a prediction value of a pixel of the HD picture is carried out by linear combination of the SD picture and a predetermined prediction coefficient, thereby restoring the high-frequency component not included in the SD picture.
Specifically, it is now assumed that, for example, a prediction value E[y] of a pixel value y of a pixel constituting the HD picture (hereinafter referred to as an HD pixel) is to be found from a linear primary combination model prescribed by linear combination of pixel values (hereinafter referred to as learning data) x
1
, x
2
, . . . of several SD pixels (pixels constituting the SD picture) and predetermined prediction coefficients w
1
, w
2
, . . . In this case, the prediction value E[y] may be expressed by Equation 1.
E[y]=w
1
x
1
+w
2
x
2
+ Equation 1
If a matrix W consisting of a set of prediction coefficients w is defined by Equation 2, and a matrix X consisting of a set of learning data is defined by Equation 3 while a matrix Y′ consisting of a set of prediction values E[y] is defined by Equation 4, in order to generalize the model, an observational equation like Equation 5 is obtained.
X
=
[
x
11
x
12
…
x
1
n
x
21
x
22
…
x
2
n
…
…
…
…
x
m1
x
m2
…
x
mn
]
Equation
2
W
=
[
w
1
w
2
…
w
n
]
Equation
3
Y
′
=
[
E
[
y
1
]
E
[
y
2
]
…
E
[
y
m
]
]
Equation
4
XW=Y
′ Equation 5
Then, it is assumed that a prediction value E[y] proximate to a pixel value y of the HD pixel is to be found by applying a minimum square method to the observational equation. In this case, if a matrix Y consisting of true pixel values y of the HD pixels to be teacher data is defined by Equation 6 while a matrix E consisting of residuals e of the prediction values E[y] with respect to the pixel values y of the HD pixels is defined by Equation 7, a residual equation like Equation 8 is obtained from Equation 5.
Y
=
[
y
1
y
2
…
y
m
]
Equation
6
Y
=
[
y
1
y
2
…
y
m
]
Equation
7
XW=Y+E
Equation 8
In this case, a prediction coefficient w
i
for finding the prediction value E[y] proximate to the pixel value y of the HD pixel may be found by minimizing the square error expressed by Formula 9.
∑
i
-
1
m
e
i
2
Formula
9
Therefore, if the value obtained by differentiating the square error of Formula 9 by the prediction coefficient w
i
is 0, the prediction value w
i
satisfying Equation 10 is the optimum value for finding the prediction value E[y] proximate to the pixel value y of the HD pixel.
e
1
∂
e
1
∂
w
i
+
e
2
∂
e
2
∂
w
i
+
…
+
e
m
∂
e
m
∂
w
i
=
0
(
i
=
1
,
2
,
…
,
n
)
Equation
10
Thus, by differentiating Equation 8 by the prediction coefficient w
1
, Equation 11 is obtained.
∂
e
i
∂
w
1
=
x
i1
,
∂
e
i
∂
w
2
=
x
i2
,
…
+
∂
e
i
∂
w
n
=
x
in
(
i
=
1
,
2
,
…
,
m
)
Equation
11
Equation 12 is obtained from Equations 10 and 11.
∑
i
=
1
m
e
i
x
i1
=
0
,
∑
i
=
1
m
e
i
x
i2
=
0
,
…
,
∑
i
=
1
m
e
i
x
in
=
0
Equation
12
In addition, in consideration of the relation between the learning data x, the prediction coefficient w, the teacher data y and the residual e in the residual equation of Equation 8 a normal equation like Equation 13 may be obtained from Equation 12.
(
∑
i
=
1
m
x
i1
x
i1
)
w
1
+
(
∑
i
=
1
m
x
i1
x
i2
)
w
2
+
…
+
(
∑
i
=
1
m
x
i1
x
in
)
w
n
=
∑
i
=
1
m
x
i1
y
i
(
∑
i
=
1
m
x
i2
x
i1
)
w
1
+
(
∑
i
=
1
m
x
i2
x
i2
)
w
2
+
…
+
(
∑
i
=
1
m
x
i2
x
in
)
w
n
=
∑
i
=
1
m
x
i2
y
i
…
(
∑
i
=
1
m
x
in
x
i1
)
w
1
+
(
∑
i
=
1
m
x
in
x
i2
)
w
2
+
…
+
(
∑
i
=
1
m
x
in
x
in
)
w
n
=
∑
i
=
1
m
x
in
y
i
Equation
13
The normal equation of Equation 13 may be established for the same number as the number of prediction coefficients w to be found. Therefore, the optimum prediction coefficient w may be found by solving Equation 13. (However, to solve Equation 13, the matrix consisting of the coefficients according to the prediction coefficients w must be regular.) In solving Equation 13, for example, a sweep method (Gauss- Jordan elimination method) may be applied.
In the foregoing manner, the set of optimum prediction coefficients w is found. Then, by using this set of prediction coefficients w, the prediction value E[y] proximate to the pixel value y of the HD pixel is found by Equation 1. The foregoing processing is adaptive processing. (Adaptive processing includes processing to find the set of prediction coefficients w in advance and find the prediction value from the set of prediction coefficients w.)
Adaptive processing differs from interpolation processing in that a component included in the HD picture which is not included in the SD picture is reproduced. Specifically, though adaptive processing is equal to interpolation processing using the so-called interpolation filter as far as Equation 1 is concerned, the prediction coefficient w corresponding to the tap coefficient of the interpolation filter is found from so-called learning by using teacher data y, thus enabling reproduction of the component included in the HD picture. That is, a picture of high resolution may be easily obtained. This indicates that adaptive processing is processing which has a picture creation effect.
FIG. 22
shows an example of the structure of a picture converting device for converting an SD picture into an HD picture by adaptive processing as described above based on the characteristics (class) of the picture.
The SD picture is supplied to a classifying circuit
101
and a delay circuit
102
. The classifying circuit
101
sequentially uses SD pixels constituting the SD picture as notable pixels, and classifies the notable pixels into predetermined classes.
The classifying circuit
101
first forms a block (hereinafter referred to as a processing block) by collecting several SD pixels around a notable pixel, and supplies a value allocated in
Kondo Tetsujiro
Takahashi Kenji
Bell Boyd & Lloyd LLC
Britton Howard
Sony Corporation
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