分享S变换函数

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Abstract
The generalized S transform (GST), a family of reversible integer-to-integer transforms inspired by the S transform, is
proposed. This family of transforms is then studied in detail, by considering topics such as GST parameter calculation, the
) d+ u* L: m0 |  Z5 `7 ^effects of using different rounding operators in the GST, and the relationship between the GST and the lifting scheme. Some
+ |6 `; m' e6 V8 s" Eexamples of specific transforms in the GST family are also given. In particular, a new transform in this family is introduced,
/ T0 m, Y+ W% Uand its practical utility demonstrated.
7 [# Q5 T0 F9 e  a3 T+ PI. I NTRODUCTION
% r' I/ L% ^+ D8 XReversible integer-to-integer transforms have become a popular tool for use in signal coding applications requir-
ing lossless signal reproduction [1–5]. One of the best known transforms of this type is the S transform [3,4,6]. In
this manuscript, we propose the generalized S transform (GST), a family of reversible integer-to-integer transforms
based on the key ideas behind the S transform. We then study the GST in some detail. This leads to a number of
4 O2 r; ^" q# u% p, G+ A) {interesting insights about transforms belonging to the GST family (including the S transform amongst others) and
reversible integer-to-integer transforms in general.
The remainder of this manuscript is structured as follows. We begin, in Section II, with a brief discussion of
7 e  T4 p4 R9 y4 z8 i& D+ t" Ethe notation and terminology used herein. The S transform is then introduced in Section III, and the GST family
of transforms is defi ned in Section IV. Sections V and VI proceed to examine GST parameter calculation and
' R3 L, a7 I& |: Nthe effects of using different rounding operators in the GST. Some examples of well known transforms belonging
to the GST family are given in Section VII, and in Section VIII, we present a new GST-based transform, and
demonstrate its utility for image coding applications. Finally, we conclude in Section IX with a summary of our
- L6 U. z# C( O3 j$ Uresults and some closing remarks.
II. N OTATION AND T ERMINOLOGY
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S变换函数