LOCO-I：低复杂度无损图像压缩算法解析
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"这篇文档主要介绍了LOCO-I，一种低复杂度、基于上下文的无损图像压缩算法。该算法由Marcel J. Weinberger、Gadiel Seroussi和Guillermo Sapozhnikov在Hewlett-Packard Laboratories开发，旨在结合霍夫曼编码的简单性和上下文模型的压缩潜力，提供高效且无损的图像压缩方案。"
在图像处理领域，无损压缩是一种重要的技术，它能够在不损失原始数据的情况下对图像进行压缩和解压缩，这对于需要保持原始质量的应用如医学影像、科学数据或数字取证等至关重要。LOCO-I（Low Complexity Lossless Compression for Images）正是这样一种算法，它通过简单的固定上下文模型来接近更复杂的通用上下文建模技术，有效捕捉高阶依赖性。
LOCO-I算法的核心是结合了霍夫曼编码和上下文模型。霍夫曼编码是一种经典的变长编码方法，它根据符号出现的频率分配不同的位数，频繁出现的符号用较少的位表示，从而提高压缩效率。而上下文模型则用于预测图像中的像素值，通过分析相邻像素的模式来改进预测的准确性，进一步提升压缩比。
LOCO-I使用一个适应性的、基于符号的Golomb-Rice编码来实现这些上下文条件的霍夫曼码。Golomb-Rice编码是一种适合编码非负整数的统计编码方法，尤其适用于具有特定分布特征的数据，如图像中的像素值。这种编码方式允许算法在单次扫描中，无需采用更高复杂度的算术编码，就能达到与当前最先进的基于算术编码的压缩方案相当甚至更优的压缩比率。
由于其高效的性能和相对较低的计算复杂度，LOCO-I被ISO委员会考虑作为现有无损压缩标准的替代选项。这表明LOCO-I不仅在理论上有其优势，而且在实际应用中也具备广泛的潜力，可能成为未来图像压缩标准的一部分。
LOCO-I算法是无损图像压缩领域的创新之作，它通过结合简单编码策略和上下文模型，实现了高效率和高压缩比的平衡，对于需要高质量图像保存的领域具有重要意义。在理解这篇文档时，读者需要对图像处理的基本原理、霍夫曼编码、上下文模型以及Golomb-Rice编码有一定的了解。
LOCO-I: A Low Complexity, Context-Based,
Lossless Image Compression Algorithm
Marcel0
J.
Weinberger, Gadiel Seroussi, and Guillermo Sapzro
Hewlett-Packard Laboratories, Palo Alto,
CA
94304
Abstract.
LOCO-I (LOW Complexity Lossless Compression for Images) is a novel loss-
less compression algorithm for continuous-tone images which combines the simplicity
of
Huffman coding with the compression potential
of
context models, thus “enjoying the best
of both worlds.” The algorithm is based on
a
simple fixed context model, which approaches
the capability
of
the more complex universal context modeling techniques for capturing
high-order dependencies. The model
is
tuned for efficient performance in conjunction with
a collection
of
(context-conditioned) Huffman codes, which is realized with an adaptive,
symbol-wise, Golomb-Rice code.
LOCO-I
attains, in one pass, and without recourse to
the higher complexity arithmetic coders, compression ratios similar or superior to those
obtained with state-of-the-art schemes based
on
arithmetic coding. In fact, LOCO-I is be-
ing considered by the
IS0
committee
as
a replacement
for
the current lossless standard in
low-complexity applications.
1
Introduction
Lossless image compression schemes often consist of two distinct and independent
components:
modeling
and
coding.
The modeling part can be formulated as an in-
ductive inference problem, in which an image is observed pixel by pixel in some
pre-defined order (e.g., raster-scan).
At
each time instant
i,
and after having scanned
past data
xi
=
~1x2
. . .
xi,
one wishes to make inferences on the next pixel value
si+l
by assigning
a
conditional probability distribution
p(.lzz)
to it.’ Ideally, the code
length contributed by
zz+l
is
-
logp(zi+l(z’)
bits (hereafter, logarithms are taken
~
to the base
Z),
which averages to the entropy of the probabilistic model. Thus, a
skewed (low-entropy) probability distribution, which assigns
a
high probability value
to the next pixel, is desirable. In
a
sequential
formulation, the distribution
p(./z2)
is
learned from the past and it is available to the decoder as it decodes the past string
sequentially. Alternatively, in a two-pass scheme the conditional distribution can be
learned from the whole image in
a
first pass and must be sent to the decoder as header
information. In this case, the total code length includes the length of the header. Yet,
both the second encoding pass and the (single-pass) decoding are subject to the same
sequential formulation.
In principle, skewed distributions can be obtained through larger conditioning
regions or “contexts.” However, this implies
a
larger number
of
parameters
in
the
statistical model, with an associated
model cost
[l]
which could offset the entropy
savings. In a sequential scheme, this cost can be interpreted as capturing the penal-
ties of “context dilution” occurring when count statistics must be spread over too
many contexts, thus affecting the accuracy of the corresponding estimates. In non-
sequential (two-pass) schemes the model cost represents the code length required to
encode the model parameters estimated in the
first
pass, which must be transmitted
to the decoder.
In
both cases the model cost is proportional to the number
of
free
parameters in the statistical model
[2].
~ ~
1
’
~
INotice that pixel values
are indexed
with
only one
subscript, despite corresponding to
a
two-
dimensional
array.
This subscript denotes the “time”
index
in
the
pre-defined
order.
140 1068-0314/96$5.00
0
1996
IEEE
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