分享S变换函数

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Abstract
" R/ h7 f3 k/ ?, {1 m; i7 B. bThe 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
, u/ @( ^' @/ t" |effects of using different rounding operators in the GST, and the relationship between the GST and the lifting scheme. Some
. O$ v2 y# M9 d) |6 pexamples of specific transforms in the GST family are also given. In particular, a new transform in this family is introduced,
& ]) o0 _5 P8 k# Zand its practical utility demonstrated.
* D4 p: w" y2 w3 D  ~I. I NTRODUCTION
Reversible 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
8 J' p$ t* Y1 c* G. Z$ jthis 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
: M4 ]( X. E' {  F- rinteresting 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
) p0 ^& j# Y+ s( E: {5 j/ Z# s/ q& cthe notation and terminology used herein. The S transform is then introduced in Section III, and the GST family
! @9 B: D; g2 ~4 ^; e4 A% zof transforms is defi ned in Section IV. Sections V and VI proceed to examine GST parameter calculation and
the effects of using different rounding operators in the GST. Some examples of well known transforms belonging
6 E: @% v  ^" Z' I$ V/ xto the GST family are given in Section VII, and in Section VIII, we present a new GST-based transform, and
: u: o+ ^. g2 D, Q. Ydemonstrate its utility for image coding applications. Finally, we conclude in Section IX with a summary of our
& \# m9 M8 W( G6 dresults and some closing remarks.
( c% h* |! h3 z9 X2 n8 WII. N OTATION AND T ERMINOLOGY


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S变换函数