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Abstract- Y3 \. F3 r/ z: j
The generalized S transform (GST), a family of reversible integer-to-integer transforms inspired by the S transform, is
5 t# Q+ S& u7 F" Oproposed. This family of transforms is then studied in detail, by considering topics such as GST parameter calculation, the
2 r. Y& J+ b* _- @4 l# ?effects of using different rounding operators in the GST, and the relationship between the GST and the lifting scheme. Some7 J7 d2 W0 n9 q ]; [* R9 N p
examples of specific transforms in the GST family are also given. In particular, a new transform in this family is introduced,
+ T$ s9 Y7 Q8 y/ \; l' n8 j* {0 Uand its practical utility demonstrated.
5 c, u$ X* z- d% _6 p1 `1 nI. I NTRODUCTION) R2 h4 i7 r J& p3 i' S# l W, z$ m" Y
Reversible integer-to-integer transforms have become a popular tool for use in signal coding applications requir-7 j4 r8 s# p) g8 c6 Z
ing lossless signal reproduction [1–5]. One of the best known transforms of this type is the S transform [3,4,6]. In: J! l6 |, m, P: @+ h7 w
this manuscript, we propose the generalized S transform (GST), a family of reversible integer-to-integer transforms
. V0 y5 B* p, J3 _" ybased on the key ideas behind the S transform. We then study the GST in some detail. This leads to a number of
" x8 j6 E: J G; Z1 o* C$ z+ z" l( yinteresting insights about transforms belonging to the GST family (including the S transform amongst others) and0 e5 \, v, J/ f. H/ h) \
reversible integer-to-integer transforms in general., W: h/ w: T' ^8 t7 U: u
The remainder of this manuscript is structured as follows. We begin, in Section II, with a brief discussion of- z+ L! S: q7 M- P/ |. R1 p9 B/ T
the notation and terminology used herein. The S transform is then introduced in Section III, and the GST family
' K& j( `* E/ b+ C( C# Uof transforms is defi ned in Section IV. Sections V and VI proceed to examine GST parameter calculation and
3 ?: z, E% G2 i, I, Vthe effects of using different rounding operators in the GST. Some examples of well known transforms belonging
2 g4 t% T% T- y' x- J9 q, S2 N1 cto the GST family are given in Section VII, and in Section VIII, we present a new GST-based transform, and
: H2 Z: n( }! U) }( {demonstrate its utility for image coding applications. Finally, we conclude in Section IX with a summary of our
# T+ j M8 r. R2 D) D6 Sresults and some closing remarks.
" V! N* i% u% n0 zII. N OTATION AND T ERMINOLOGY& c) y- c; Y* O8 H5 f
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发表于 2020-2-27 17:57
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