function?x?=?ifdct_wrapping（C?is_real?M?N）

%?ifdct_wrapping.m?-?Inverse?Fast?Discrete?Curvelet?Transform?via?wedge?wrapping?-?Version?1.0
%?This?is?in?fact?the?adjoint?also?the?pseudo-inverse
%
%?Inputs
%???C???????????Cell?array?containing?curvelet?coefficients?（see
%???????????????description?in?fdct_wrapping.m）
%???is_real?????As?used?in?fdct_wrapping.m
%???M?N????????Size?of?the?image?to?be?recovered?（not?necessary?if?finest
%???????????????=?2）
%
%?Outputs
%???x???????????M-by-N?matrix
%
%?See?also?fdct_wrapping.m
%
%?By?Laurent?Demanet?2004

%?Initialization
nbscales?=?length（C）;
nbangles_coarse?=?length（C{2}）;
nbangles?=?[1?nbangles_coarse?.*?2.^（ceil（（nbscales-（nbscales:-1:2））/2））];
if?length（C{end}）?==?1?finest?=?2;?else?finest?=?1;?end;
if?finest?==?2?nbangles（nbscales）?=?1;?end;
if?nargin?if?nargin?????if?finest?==?1?error（‘Syntax:?IFCT_wrapping（CMN）?where?the?matrix?to?be?recovered?is?M-by-N‘）;?end;
????[N1N2]?=?size（C{end}{1}）;
else
????N1?=?M;
????N2?=?N;
end;

M1?=?N1/3;
M2?=?N2/3;

if?finest?==?1;
????
????bigN1?=?2*floor（2*M1）+1;
????bigN2?=?2*floor（2*M2）+1;
????X?=?zeros（bigN1bigN2）;

????%?Initialization:?preparing?the?lowpass?filter?at?finest?scale
????window_length_1?=?floor（2*M1）?-?floor（M1）?-?1?-?（mod（N13）==0）;
????window_length_2?=?floor（2*M2）?-?floor（M2）?-?1?-?（mod（N23）==0）;
????coord_1?=?0:（1/window_length_1）:1;
????coord_2?=?0:（1/window_length_2）:1;
????[wl_1wr_1]?=?fdct_wrapping_window（coord_1）;
????[wl_2wr_2]?=?fdct_wrapping_window（coord_2）;
????lowpass_1?=?[wl_1?ones（12*floor（M1）+1）?wr_1];
????if?mod（N13）==0?lowpass_1?=?[0?lowpass_1?0];?end;
????lowpass_2?=?[wl_2?ones（12*floor（M2）+1）?wr_2];
????if?mod（N23）==0?lowpass_2?=?[0?lowpass_2?0];?end;
????lowpass?=?lowpass_1‘*lowpass_2;

????scales?=?nbscales:-1:2;
???
else

????M1?=?M1/2;
????M2?=?M2/2;
????
????bigN1?=?2*floor（2*M1）+1;
????bigN2?=?2*floor（2*M2）+1;
????X?=?zeros（bigN1bigN2）;
????
????window_length_1?=?floor（2*M1）?-?floor（M1）?-?1;
????window_length_2?=?floor（2*M2）?-?floor（M2）?-?1;
????coord_1?=?0:（1/window_length_1）:1;
????coord_2?=?0:（1/window_length_2）:1;
????[wl_1wr_1]?=?fdct_wrapping_window（coord_1）;
????[wl_2wr_2]?=?fdct_wrapping_window（coord_2）;
????lowpass_1?=?[wl_1?ones（12*floor（M1）+1）?wr_1];
????lowpass_2?=?[wl_2?ones（12*floor（M2）+1）?wr_2];
????lowpass?=?lowpass_1‘*lowpass_2;
????hipass_finest?=?sqrt（1?-?lowpass.^2）;
????
????scales?=?（nbscales-1）:-1:2;
????
end;

%?Loop:?pyramidal?reconstruction

Xj_topleft_1?=?1;
Xj_topleft_2?=?1;
for?j?=?scales

????M1?=?M1/2;
????M2?=?M2/2;
????window_length_1?=?floor（2*M1）?-?floor（M1）?-?1;
????window_length_2?=?floor（2*M2）?-?floor（M2）?-?1;
????coord_1?=?0:（1/window_length_1）:1;
????coord_2?=?0:（1/window_length_2）:1;
????[wl_1wr_1]?=?fdct_wrapping_window（coord_1）;
????[wl_2wr_2]?=?fdct_wrapping_window（coord_2）;
????lowpass_1?=?[wl_1?ones（12*floor（M1）+1）?wr_1];
????lowpass_2?=?[wl_2?ones（12*floor（M2）+1）?wr_2];
????lowpass_next?=?lowpass