/** computes the inverse discrete Radon transform of Rf
* on the grid given by gridfcn() with T angles and R offsets
* by a NFFT-based CG-type algorithm
*/
int Inverse_Radon_trafo(int (*gridfcn)(), int T, int S, double *Rf, int NN, double *f, int max_i)
{
int j,k; /**< index for nodes and freqencies */
nfft_plan my_nfft_plan; /**< plan for the nfft-2D */
solver_plan_complex my_infft_plan; /**< plan for the inverse nfft */
fftw_complex *fft; /**< variable for the fftw-1Ds */
fftw_plan my_fftw_plan; /**< plan for the fftw-1Ds */
int t,r; /**< index for directions and offsets */
double *x, *w; /**< knots and associated weights */
int l; /**< index for iterations */
int N[2],n[2];
int M=T*S;
N[0]=NN; n[0]=2*N[0];
N[1]=NN; n[1]=2*N[1];
fft = (fftw_complex *)nfft_malloc(S*sizeof(fftw_complex));
my_fftw_plan = fftw_plan_dft_1d(S,fft,fft,FFTW_FORWARD,FFTW_MEASURE);
x = (double *)nfft_malloc(2*T*S*(sizeof(double)));
if (x==NULL)
return -1;
w = (double *)nfft_malloc(T*S*(sizeof(double)));
if (w==NULL)
return -1;
/** init two dimensional NFFT plan */
nfft_init_guru(&my_nfft_plan, 2, N, M, n, 4,
PRE_PHI_HUT| PRE_PSI| MALLOC_X | MALLOC_F_HAT| MALLOC_F| FFTW_INIT | FFT_OUT_OF_PLACE,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
/** init two dimensional infft plan */
solver_init_advanced_complex(&my_infft_plan,(nfft_mv_plan_complex*)(&my_nfft_plan), CGNR | PRECOMPUTE_WEIGHT);
/** init nodes and weights of grid*/
gridfcn(T,S,x,w);
for(j=0;j<my_nfft_plan.M_total;j++)
{
my_nfft_plan.x[2*j+0] = x[2*j+0];
my_nfft_plan.x[2*j+1] = x[2*j+1];
if (j%S)
my_infft_plan.w[j] = w[j];
else
my_infft_plan.w[j] = 0.0;
}
/** precompute psi, the entries of the matrix B */
if(my_nfft_plan.nfft_flags & PRE_LIN_PSI)
nfft_precompute_lin_psi(&my_nfft_plan);
if(my_nfft_plan.nfft_flags & PRE_PSI)
nfft_precompute_psi(&my_nfft_plan);
if(my_nfft_plan.nfft_flags & PRE_FULL_PSI)
nfft_precompute_full_psi(&my_nfft_plan);
/** compute 1D-ffts and init given samples and weights */
for(t=0; t<T; t++)
{
/* for(r=0; r<R/2; r++)
fft[r] = cexp(I*KPI*r)*Rf[t*R+(r+R/2)];
for(r=0; r<R/2; r++)
fft[r+R/2] = cexp(I*KPI*r)*Rf[t*R+r];
*/
for(r=0; r<S; r++)
fft[r] = Rf[t*S+r] + _Complex_I*0.0;
nfft_fftshift_complex(fft, 1, &S);
fftw_execute(my_fftw_plan);
nfft_fftshift_complex(fft, 1, &S);
my_infft_plan.y[t*S] = 0.0;
for(r=-S/2+1; r<S/2; r++)
my_infft_plan.y[t*S+(r+S/2)] = fft[r+S/2]/KERNEL(r);
}
/** initialise some guess f_hat_0 */
for(k=0;k<my_nfft_plan.N_total;k++)
my_infft_plan.f_hat_iter[k] = 0.0 + _Complex_I*0.0;
/** solve the system */
solver_before_loop_complex(&my_infft_plan);
if (max_i<1)
{
l=1;
for(k=0;k<my_nfft_plan.N_total;k++)
my_infft_plan.f_hat_iter[k] = my_infft_plan.p_hat_iter[k];
}
else
{
for(l=1;l<=max_i;l++)
{
solver_loop_one_step_complex(&my_infft_plan);
/*if (sqrt(my_infft_plan.dot_r_iter)<=1e-12) break;*/
}
}
/*printf("after %d iteration(s): weighted 2-norm of original residual vector = %g\n",l-1,sqrt(my_infft_plan.dot_r_iter));*/
/** copy result */
for(k=0;k<my_nfft_plan.N_total;k++)
f[k] = creal(my_infft_plan.f_hat_iter[k]);
/** finalise the plans and free the variables */
fftw_destroy_plan(my_fftw_plan);
nfft_free(fft);
solver_finalize_complex(&my_infft_plan);
nfft_finalize(&my_nfft_plan);
nfft_free(x);
nfft_free(w);
return 0;
}
/** computes the inverse discrete Radon transform of Rf
* on the grid given by gridfcn() with T angles and R offsets
* by a NFFT-based CG-type algorithm
*/
static int inverse_radon_trafo(int (*gridfcn)(), int T, int S, NFFT_R *Rf, int NN, NFFT_R *f,
int max_i)
{
int j, k; /**< index for nodes and freqencies */
NFFT(plan) my_nfft_plan; /**< plan for the nfft-2D */
SOLVER(plan_complex) my_infft_plan; /**< plan for the inverse nfft */
NFFT_C *fft; /**< variable for the fftw-1Ds */
FFTW(plan) my_fftw_plan; /**< plan for the fftw-1Ds */
int t, r; /**< index for directions and offsets */
NFFT_R *x, *w; /**< knots and associated weights */
int l; /**< index for iterations */
int N[2], n[2];
int M = T * S;
N[0] = NN;
n[0] = 2 * N[0];
N[1] = NN;
n[1] = 2 * N[1];
fft = (NFFT_C *) NFFT(malloc)((size_t)(S) * sizeof(NFFT_C));
my_fftw_plan = FFTW(plan_dft_1d)(S, fft, fft, FFTW_FORWARD, FFTW_MEASURE);
x = (NFFT_R *) NFFT(malloc)((size_t)(2 * T * S) * (sizeof(NFFT_R)));
if (x == NULL)
return EXIT_FAILURE;
w = (NFFT_R *) NFFT(malloc)((size_t)(T * S) * (sizeof(NFFT_R)));
if (w == NULL)
return EXIT_FAILURE;
/** init two dimensional NFFT plan */
NFFT(init_guru)(&my_nfft_plan, 2, N, M, n, 4,
PRE_PHI_HUT | PRE_PSI | MALLOC_X | MALLOC_F_HAT | MALLOC_F | FFTW_INIT
| FFT_OUT_OF_PLACE,
FFTW_MEASURE | FFTW_DESTROY_INPUT);
/** init two dimensional infft plan */
SOLVER(init_advanced_complex)(&my_infft_plan,
(NFFT(mv_plan_complex)*) (&my_nfft_plan), CGNR | PRECOMPUTE_WEIGHT);
/** init nodes and weights of grid*/
gridfcn(T, S, x, w);
for (j = 0; j < my_nfft_plan.M_total; j++)
{
my_nfft_plan.x[2 * j + 0] = x[2 * j + 0];
my_nfft_plan.x[2 * j + 1] = x[2 * j + 1];
if (j % S)
my_infft_plan.w[j] = w[j];
else
my_infft_plan.w[j] = NFFT_K(0.0);
}
/** precompute psi, the entries of the matrix B */
if (my_nfft_plan.flags & PRE_LIN_PSI)
NFFT(precompute_lin_psi)(&my_nfft_plan);
if (my_nfft_plan.flags & PRE_PSI)
NFFT(precompute_psi)(&my_nfft_plan);
if (my_nfft_plan.flags & PRE_FULL_PSI)
NFFT(precompute_full_psi)(&my_nfft_plan);
/** compute 1D-ffts and init given samples and weights */
for (t = 0; t < T; t++)
{
/* for(r=0; r<R/2; r++)
fft[r] = cexp(I*NFFT_KPI*r)*Rf[t*R+(r+R/2)];
for(r=0; r<R/2; r++)
fft[r+R/2] = cexp(I*NFFT_KPI*r)*Rf[t*R+r];
*/
for (r = 0; r < S; r++)
fft[r] = Rf[t * S + r] + _Complex_I * NFFT_K(0.0);
NFFT(fftshift_complex_int)(fft, 1, &S);
FFTW(execute)(my_fftw_plan);
NFFT(fftshift_complex_int)(fft, 1, &S);
my_infft_plan.y[t * S] = NFFT_K(0.0);
for (r = -S / 2 + 1; r < S / 2; r++)
my_infft_plan.y[t * S + (r + S / 2)] = fft[r + S / 2] / KERNEL(r);
}
/** initialise some guess f_hat_0 */
for (k = 0; k < my_nfft_plan.N_total; k++)
my_infft_plan.f_hat_iter[k] = NFFT_K(0.0) + _Complex_I * NFFT_K(0.0);
/** solve the system */
SOLVER(before_loop_complex)(&my_infft_plan);
if (max_i < 1)
{
l = 1;
for (k = 0; k < my_nfft_plan.N_total; k++)
my_infft_plan.f_hat_iter[k] = my_infft_plan.p_hat_iter[k];
}
else
{
for (l = 1; l <= max_i; l++)
{
SOLVER(loop_one_step_complex)(&my_infft_plan);
/*if (sqrt(my_infft_plan.dot_r_iter)<=1e-12) break;*/
}
}
/*printf("after %d iteration(s): weighted 2-norm of original residual vector = %g\n",l-1,sqrt(my_infft_plan.dot_r_iter));*/
/** copy result */
for (k = 0; k < my_nfft_plan.N_total; k++)
f[k] = NFFT_M(creal)(my_infft_plan.f_hat_iter[k]);
/** finalise the plans and free the variables */
FFTW(destroy_plan)(my_fftw_plan);
NFFT(free)(fft);
SOLVER(finalize_complex)(&my_infft_plan);
NFFT(finalize)(&my_nfft_plan);
NFFT(free)(x);
NFFT(free)(w);
return 0;
}
