//------------------------------------------------------------------- int fdct_wrapping(int N1, int N2, int nbscales, int nbangles_coarse, int allcurvelets, CpxNumMat& x, vector< vector<CpxNumMat> >& c) { //--------------------------------------------- assert(N1==x.m() && N2==x.n()); int F1 = N1/2; int F2 = N2/2; // ifft original data CpxNumMat T(x); fftwnd_plan p = fftw2d_create_plan(N2, N1, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE); fftwnd_one(p, (fftw_complex*)T.data(), NULL); fftwnd_destroy_plan(p); double sqrtprod = sqrt(double(N1*N2)); for(int j=0; j<N2; j++) for(int i=0; i<N1; i++) T(i,j) /= sqrtprod; CpxOffMat O(N1, N2); fdct_wrapping_fftshift(T, O); //----------------------------------------------------------------------------- vector<CpxOffMat> Xhghs; Xhghs.resize(nbscales); CpxOffMat X; //unfold or not if(allcurvelets==1) { //-------------------------- double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2); IntOffVec t1(XS1); for(int i=-XF1; i<-XF1+XS1; i++) if( i<-N1/2) t1(i) = i+int(N1); else if(i>(N1-1)/2) t1(i) = i-int(N1); else t1(i) = i; IntOffVec t2(XS2); for(int i=-XF2; i<-XF2+XS2; i++) if( i<-N2/2) t2(i) = i+int(N2); else if(i>(N2-1)/2) t2(i) = i-int(N2); else t2(i) = i; X.resize(XS1, XS2); for(int j=-XF2; j<-XF2+XS2; j++) for(int i=-XF1; i<-XF1+XS1; i++) X(i,j) = O(t1(i), t2(j)); DblOffMat lowpass(XS1,XS2); fdct_wrapping_lowpasscompute(XL1, XL2, lowpass); //compute the low pass filter for(int j=-XF2; j<-XF2+XS2; j++) for(int i=-XF1; i<-XF1+XS1; i++) X(i,j) *= lowpass(i,j); } else { //-------------------------- X = O; } //separate double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range for(int sc=nbscales-1; sc>0; sc--) { double XL1n = XL1/2; double XL2n = XL2/2; int XS1n, XS2n; int XF1n, XF2n; double XR1n, XR2n; fdct_wrapping_rangecompute(XL1n, XL2n, XS1n, XS2n, XF1n, XF2n, XR1n, XR2n); //computer filter DblOffMat lowpass(XS1n, XS2n); fdct_wrapping_lowpasscompute(XL1n, XL2n, lowpass); DblOffMat hghpass(XS1n, XS2n); for(int j=-XF2n; j<-XF2n+XS2n; j++) for(int i=-XF1n; i<-XF1n+XS1n; i++) hghpass(i,j) = sqrt(1-lowpass(i,j)*lowpass(i,j)); //separate CpxOffMat Xhgh(X); for(int j=-XF2n; j<-XF2n+XS2n; j++) for(int i=-XF1n; i<-XF1n+XS1n; i++) Xhgh(i,j) *= hghpass(i,j); CpxOffMat Xlow(XS1n, XS2n); for(int j=-XF2n; j<-XF2n+XS2n; j++) for(int i=-XF1n; i<-XF1n+XS1n; i++) Xlow(i,j) = X(i,j) * lowpass(i,j); //store and prepare for next level Xhghs[sc] = Xhgh; X = Xlow; XL1 = XL1/2; XL2 = XL2/2; } Xhghs[0] = X; //----------------------------------------------------------------------------- vector<int> nbangles(nbscales); if(allcurvelets==1) { //nbangles nbangles[0] = 1; for(int sc=1; sc<nbscales; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) ); //c c.resize(nbscales); for(int sc=0; sc<nbscales; sc++) c[sc].resize( nbangles[sc] ); double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range for(int sc=nbscales-1; sc>0; sc--) { fdct_wrapping_sepangle(XL1, XL2, nbangles[sc], Xhghs[sc], c[sc]); XL1 /= 2; XL2 /= 2; } fdct_wrapping_wavelet(Xhghs[0], c[0]); } else { //nbangles nbangles[0] = 1; for(int sc=1; sc<nbscales-1; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) ); nbangles[nbscales-1] = 1; //c c.resize(nbscales); for(int sc=0; sc<nbscales; sc++) c[sc].resize( nbangles[sc] ); fdct_wrapping_wavelet(Xhghs[nbscales-1], c[nbscales-1]); double XL1 = 2.0*N1/3.0; double XL2 = 2.0*N2/3.0; //range for(int sc=nbscales-2; sc>0; sc--) { fdct_wrapping_sepangle(XL1, XL2, nbangles[sc], Xhghs[sc], c[sc]); XL1 /= 2; XL2 /= 2; } fdct_wrapping_wavelet(Xhghs[0], c[0]); } return 0; }
//------------------------------------------------------------------------------- int ifdct_wrapping(int N1, int N2, int nbscales, int nbangles_coarse, int allcurvelets, vector< vector<CpxNumMat> >& c, CpxNumMat& x) { assert(nbscales==c.size() && nbangles_coarse==c[1].size()); //int F1 = N1/2; int F2 = N2/2; //-------------------------------------------angles to Xhgh vector<int> nbangles(nbscales); vector<CpxOffMat> Xhghs; Xhghs.resize(nbscales); if(allcurvelets==1) { //---- nbangles[0] = 1; for(int sc=1; sc<nbscales; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) ); double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; for(int sc=nbscales-1; sc>0; sc--) { fdct_wrapping_invsepangle(XL1, XL2, nbangles[sc], c[sc], Xhghs[sc]); XL1 /= 2; XL2 /= 2; } fdct_wrapping_invwavelet(c[0], Xhghs[0]); } else { //---- nbangles[0] = 1; for(int sc=1; sc<nbscales-1; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) ); nbangles[nbscales-1] = 1; fdct_wrapping_invwavelet(c[nbscales-1], Xhghs[nbscales-1]); double XL1 = 2.0*N1/3.0; double XL2 = 2.0*N2/3.0; for(int sc=nbscales-2; sc>0; sc--) { fdct_wrapping_invsepangle(XL1, XL2, nbangles[sc], c[sc], Xhghs[sc]); XL1 /= 2; XL2 /= 2; } fdct_wrapping_invwavelet(c[0], Xhghs[0]); } //-------------------------------------------xhghs to O //combine CpxOffMat X; if(allcurvelets==1) { double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2); X.resize(XS1, XS2); } else { X.resize(N1, N2); } double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2); for(int sc=nbscales-1; sc>0; sc--) { double XL1n = XL1/2; double XL2n = XL2/2; int XS1n, XS2n; int XF1n, XF2n; double XR1n, XR2n; fdct_wrapping_rangecompute(XL1n, XL2n, XS1n, XS2n, XF1n, XF2n, XR1n, XR2n); DblOffMat lowpass(XS1n, XS2n); fdct_wrapping_lowpasscompute(XL1n, XL2n, lowpass); DblOffMat hghpass(XS1n, XS2n); for(int j=-XF2n; j<-XF2n+XS2n; j++) for(int i=-XF1n; i<-XF1n+XS1n; i++) hghpass(i,j) = sqrt(1-lowpass(i,j)*lowpass(i,j)); for(int j=-XF2n; j<-XF2n+XS2n; j++) for(int i=-XF1n; i<-XF1n+XS1n; i++) Xhghs[sc](i,j) *= hghpass(i,j); for(int j=-XF2n; j<-XF2n+XS2n; j++) for(int i=-XF1n; i<-XF1n+XS1n; i++) Xhghs[sc-1](i,j) *= lowpass(i,j); CpxOffMat& G = Xhghs[sc]; for(int j=G.t(); j<G.t()+G.n(); j++) for(int i=G.s(); i<G.s()+G.m(); i++) X(i,j) += G(i,j); XL1 = XL1/2; XL2 = XL2/2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2); } for(int j=-XF2; j<-XF2+XS2; j++) for(int i=-XF1; i<-XF1+XS1; i++) X(i,j) += Xhghs[0](i,j); // fold CpxOffMat O(N1, N2); if(allcurvelets==1) { double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2); //times pou; DblOffMat lowpass(XS1,XS2); fdct_wrapping_lowpasscompute(XL1, XL2, lowpass); for(int j=-XF2; j<-XF2+XS2; j++) for(int i=-XF1; i<-XF1+XS1; i++) X(i,j) *= lowpass(i,j); IntOffVec t1(XS1); for(int i=-XF1; i<-XF1+XS1; i++) if( i<-N1/2) t1(i) = i+int(N1); else if(i>(N1-1)/2) t1(i) = i-int(N1); else t1(i) = i; IntOffVec t2(XS2); for(int i=-XF2; i<-XF2+XS2; i++) if( i<-N2/2) t2(i) = i+int(N2); else if(i>(N2-1)/2) t2(i) = i-int(N2); else t2(i) = i; for(int j=-XF2; j<-XF2+XS2; j++) for(int i=-XF1; i<-XF1+XS1; i++) O(t1(i), t2(j)) += X(i,j); } else { O = X; } //------------------------------------------------------------ CpxNumMat T(N1,N2); fdct_wrapping_ifftshift(O, T); fftwnd_plan p = fftw2d_create_plan(N2, N1, FFTW_BACKWARD, FFTW_ESTIMATE | FFTW_IN_PLACE); fftwnd_one(p, (fftw_complex*)T.data(), NULL); fftwnd_destroy_plan(p); double sqrtprod = sqrt(double(N1*N2)); //scale for(int i=0; i<N1; i++) for(int j=0; j<N2; j++) T(i,j) /= sqrtprod; x = T; //x.resize(N1, N2); //fdct_wrapping_fftshift(T, x); return 0; }