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decoded image, but also can save bits due to providing high-quality reference frames
for succeeding images. Compared with SAO, adaptive loop filter takes more filter
taps to convolve with the reconstructed pixels. It is usually located as the last process-
ing stage of each picture (Tsai et al.
2013
). The filter coefficients are obtained by
minimizing the mean square error between original samples and decoded samples,
which can be formulated as the following optimization problem,
⊛
⊞
⊝
I
x
,
y
−
f
i
,
j
I
x
+
i
,
y
+
j
⊠
,
f
=
argmin
f
(7.23)
=
{
}
f
i
,
j
x
y
i
,
j
where
f
i
,
j
is the filter coefficient of a 2D filter, and
I
x
,
y
and
I
x
,
y
are the original pixel
and the output reconstructed pixels from the previous in-loop filter, e.g., SAO. By
applying the adaptive loop filter to the compressed frame, the filtered frame becomes
closer to the original frame.
There aremainly three types of ALF, i.e., frame-based, block-based, and quadtree-
based ALFs. In Chiu and Xu (
2008
), a frame-based ALF is proposed and one picture-
level flag is employed to control the filter on/off. Although ALF is able to improve the
reconstructed image quality on the whole, it may degrade image quality in some local
areas. Therefore, a block-based ALF (BALF) is proposed in Chujoh et al. (
2008
).
BALF applies a filter to luminance blocks and a flag to indicate whether the block
is filtered is signaled. Therefore, BALF improves the flexibility of ALF to adapt to
different areas. The quadtree-based ALF (QALF) further improves ALF efficiency
by signaling the filter switch flag in a quadtree data structure to carry out the variable
block size filtering (Chujoh et al.
2009
).
In HEVC, a modified QALF is proposed in Karczewicz et al. (
2010
). Instead
of applying a single filter, multiple filters (up to 16 filters) are employed for each
frame. It first classifies the pixel into multiple categories by applying a sum-modified
Laplacian measure to each pixel, and then trains each filter with pixels in one cat-
egory. The number of filters for each frame is also adaptively determined based on
the rate-distortion optimization at encoder side. Therefore, adaptive filter parame-
ter merging process is introduced at the encoder. In order to reduce the redundancy
among multiple filter coefficients in each frame, differential coding is applied in filter
coefficients coding.
Due to the complexity of pixel classification, two other pixel classification meth-
ods, block-based (BA) and region-based (RA), are proposed in Chong et al. (
2011
),
Chen et al. (
2011
), respectively. The BA method classifies all the pixels in one block
(i.e., 4
4 block based) into one category based on the average Laplacian-based
activity metrics, which can decrease the switch frequency of ALF at the decoder.
The RA method divides the picture into 16 roughly-equal-size regions where each
region is aligned with largest coding unit (LCU) boundaries, which significantly
reduces the computation cost for classification.
Considering the redundancy of ALF parameters between frames, a temporal coef-
ficients reuse scheme is proposed in HEVC (Zhang et al.
2012
) to further improve
the ALF efficiency. In Wenger et al. (
2011
), a new syntax structure for ALF and
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