function x = iwa1(c,pat,tp)% iwa1 - inverse wave atom transform% -----------------% INPUT% --% c is a cell array which contains the wave atom coefficients. If% tp=='ortho', then c{j}{m}(n) is the coefficient at scale j, frequency% index m and spatial index n If tp=='complex', then c{j,1}c{j}{m}(n)% and c{j,2}c{j}{m}(n) are the coefficients at scale j, frequency index% m and spatial index n.% --% pat specifies the type of frequency partition which satsifies% parabolic scaling relationship. pat can either be 'p' or 'q'.% --% tp is the type of tranform.% 	'ortho': orthobasis% 	'complex': complex-valued frame with redunancy 2.% -----------------% OUTPUT% --% x is a real N-by-1 vector. N is a power of 2.% -----------------% Written by Lexing Ying and Laurent Demanet, 2007  if( ismember(tp, {'ortho','directional','complex'})==0 | ismember(pat, {'p','q','u'})==0 )    error('wrong');  end    if(strcmp(tp, 'ortho')==1)    %---------------------------------------------------------    T = 0;    for s=1:length(c)      nw = length(c{s});      for I=1:nw        T = T + prod(size(c{s}{I}));      end    end    N = T;    H = N/2;    lst = freq_pat(H,pat);    A = N;    f = zeros(A,1);    %------------------    for s=1:length(lst)      nw = length(lst{s});      for I=0:nw-1        if(~isempty(c{s}{I+1}))          B = 2^(s-1);          D = 2*B;          Ict = I*B;          if(mod(I,2)==0)            Ifm = Ict-2/3*B;        Ito = Ict+4/3*B;          else            Ifm = Ict-1/3*B;        Ito = Ict+5/3*B;          end          res = fft(c{s}{I+1}) / sqrt(prod(size(c{s}{I+1})));          for id=0:1            if(id==0)              Idx = [ceil(Ifm):floor(Ito)];      Icf = kf_rt(Idx/B*pi, I);            else              Idx = [ceil(-Ito):floor(-Ifm)];      Icf = kf_lf(Idx/B*pi, I);            end            f(mod(Idx,A)+1) = f(mod(Idx,A)+1) + ( Icf.' ) .* res(mod(Idx,D)+1);          end        end      end    end    %------------------    x = ifft(f) * sqrt(prod(size(f)));  elseif(strcmp(tp, 'directional')==1)    %---------------------------------------------------------    error('wrong argument for tp');  elseif(strcmp(tp, 'complex')==1)    %---------------------------------------------------------    c1 = c(:,1);    c2 = c(:,2);        T = 0;    for s=1:length(c1)      nw = length(c1{s});      for I=1:nw        T = T + prod(size(c1{s}{I}));      end    end    N = T;    H = N/2;    lst = freq_pat(H,pat);    A = N;    f = zeros(A,1);    %------------------    for s=1:length(lst)      nw = length(lst{s});      for I=0:nw-1        if(~isempty(c1{s}{I+1}))          B = 2^(s-1);          D = 2*B;                    Ict = I*B;          if(mod(I,2)==0)            Ifm = Ict-2/3*B;        Ito = Ict+4/3*B;          else            Ifm = Ict-1/3*B;        Ito = Ict+5/3*B;          end                    Idx = [ceil(Ifm):floor(Ito)];      Icf = kf_rt(Idx/B*pi, I);          res = fft(c1{s}{I+1}) / sqrt(prod(size(c1{s}{I+1})));          f(mod(Idx,A)+1) = f(mod(Idx,A)+1) + ( Icf.' ) .* res(mod(Idx,D)+1);                    Idx = [ceil(-Ito):floor(-Ifm)];      Icf = kf_lf(Idx/B*pi, I);          res = fft(c2{s}{I+1}) / sqrt(prod(size(c2{s}{I+1})));          f(mod(Idx,A)+1) = f(mod(Idx,A)+1) + ( Icf.' ) .* res(mod(Idx,D)+1);        end      end    end    %------------------    x = ifft(f) * sqrt(prod(size(f)));  end