分享S变换函数

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Abstract
! l5 e. u. M$ W. E; vThe generalized S transform (GST), a family of reversible integer-to-integer transforms inspired by the S transform, is
! l7 i/ Y/ k8 a/ U; i9 Vproposed. This family of transforms is then studied in detail, by considering topics such as GST parameter calculation, the
% G4 x2 t8 z$ p- N- e5 F+ Teffects of using different rounding operators in the GST, and the relationship between the GST and the lifting scheme. Some
# F8 u) o  F0 j. Z. a) \: }5 z: x& ~examples of specific transforms in the GST family are also given. In particular, a new transform in this family is introduced,
and its practical utility demonstrated.
6 E0 |/ Q6 Y3 k5 r) o& mI. I NTRODUCTION
3 q4 g% @! v5 G1 p* gReversible integer-to-integer transforms have become a popular tool for use in signal coding applications requir-
! g# D! [  i2 V2 i, O) L* n# S: fing 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
9 w! N0 k# q' I7 U5 Wbased on the key ideas behind the S transform. We then study the GST in some detail. This leads to a number of
interesting insights about transforms belonging to the GST family (including the S transform amongst others) and
reversible integer-to-integer transforms in general.
! Z0 @2 E, ]* N6 iThe remainder of this manuscript is structured as follows. We begin, in Section II, with a brief discussion of
+ J5 d* e, _9 V# k% o7 I5 T7 z8 }the notation and terminology used herein. The S transform is then introduced in Section III, and the GST family
( T7 d! t) t1 X' k* |of transforms is defi ned in Section IV. Sections V and VI proceed to examine GST parameter calculation and
; B) @% F5 K+ mthe effects of using different rounding operators in the GST. Some examples of well known transforms belonging
8 j$ Z5 W" F/ c. ?+ f' G$ l: ito 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
8 ~0 i: A2 X7 `3 t* A9 [results and some closing remarks.
1 c. g3 z* q+ c! c" j1 [II. N OTATION AND T ERMINOLOGY

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S变换函数