function?[Xrhoeta]?=?art（Abk）
%ART??Algebraic?reconstruction?technique?（Kaczmarz‘s?method）.
%
%?[Xrhoeta]?=?art（Abk）
%
%?Classical?Kaczmarz?iteration?or?ART?（algebraic?reconstruction
%?technique）?applied?to?the?system?A?x?=?b.??The?number?of
%?iterations?is?k.

%?Reference:?F.?Natterer?and?F.?W黚beling?Mathematical?Methods
%?in?Image?Reconstruction?SIAM?Philadelphia?2001;?Sect.?5.3.1.

%?Per?Christian?Hansen?IMM?Dec.?6?2006.

%?Initialization.
if?（k?[mn]?=?size（A）;?X?=?zeros（nk）;
if?（nargout?>?1）
???eta?=?zeros（k1）;?rho?=?eta;
end

%?Prepare?for?iteration.
x?=?zeros（n1）;
%nai2?=?full（sum（A.*A2））;
nai2?=?full（sum（abs（A.*A）2））;
I?=?find（nai2>0）‘;

%?Iterate.
for?j=1:k
???for?i=I
??????Ai?=?full（A（i:））;
??????x?=?x?+?（b（i）-Ai*x）*Ai‘/nai2（i）;
???end
???if?（nargout?>?1）
??????eta（j）?=?norm（x）;?rho（j）?=?norm（b-A*x）;
???end
???X（:j）?=?x;
end

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件????????963??2007-09-19?19:57??art.m

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??????????????????963????????????????????1