KaiserBessel Class Reference

#include <xmipp_funcs.h>

Public Member Functions
	KaiserBessel (double alpha_, int K, double r_, double v_, int N_, double vtable_=0., int ntable_=5999)
double	I0table_maxerror ()
std::vector< double >	dump_table () const
double	sinhwin (double x) const
double	i0win (double x) const
double	i0win_tab (double x) const
int	get_window_size () const

Protected Member Functions
void	build_I0table ()

Protected Attributes
double	alpha
double	v
double	r
int	N
int	K
double	vtable
int	ntable
std::vector< double >	i0table
double	dtable
double	alphar
double	fac
double	vadjust
double	facadj
double	fltb

Detailed Description

Kaiser-Bessel function

This code was modified from SPARX and originally written by Pawel Penczek at the University of Texas - Houston Medical School

see P. A. Penczek, R. Renka, and H. Schomberg, J. Opt. Soc. Am. 21, 449 (2004)

The I0 version can be tabulated and interpolated upon demand, but the max error needs to be checked. The "vtable" parameter corresponds to the maximum value of x for which the I0 selfWindow is non-zero. Setting "vtable" different from "v" corresponds to a change in units of x. In practice, it is often handy to replace x in some sort of absolute units with x described in terms of grid intervals.

The get_kbsinh_win and get_kbi0_win functions return single-argument function objects, which is what a generic routine is likely to want.

kb = KaiserBessel(alpha, K, r, v , N);
double wx = kb.sinhwin(32);
double tablex1 = kb.i0win_tab(delx-inxold+3);

Definition at line 149 of file xmipp_funcs.h.

Constructor & Destructor Documentation

KaiserBessel()

KaiserBessel::KaiserBessel	(	double	alpha_,
		int	K,
		double	r_,
		double	v_,
		int	N_,
		double	vtable_ = 0.,
		int	ntable_ = 5999
	)

Constructor with parameters

Definition at line 53 of file xmipp_funcs.cpp.

        : alpha(alpha_), v(v_), r(r_), N(N_), K(K_), vtable(vtable_),
        ntable(ntable_)
{
    // Default values are alpha=1.25, K=6, r=0.5, v = K/2
    if (0.f == v)
        v = double(K)/2;
    if (0.f == vtable)
        vtable = v;
    alphar = alpha*r;
    fac = static_cast<double>(2.*PI)*alphar*v;
    vadjust = 1.0f*v;
    facadj = static_cast<double>(2.*PI)*alphar*vadjust;
    build_I0table();
}

Member Function Documentation

build_I0table()

void KaiserBessel::build_I0table ( )

protected

2*pi*alpha*r*vadjust

Definition at line 83 of file xmipp_funcs.cpp.

{
    i0table.resize(ntable+1); // i0table[0:ntable]
    int ltab = int(ROUND(double(ntable)/1.25f));
    fltb = double(ltab)/(K/2);
    //double val0 = gsl_sf_bessel_I0(facadj);
    double val0 = bessi0(facadj);
    for (int i=ltab+1; i <= ntable; i++)
        i0table[i] = 0.f;
    for (int i=0; i <= ltab; i++)
    {
        double s = double(i)/fltb/N;
        if (s < vadjust)
        {
            double rt = sqrt(1.f - pow(s/vadjust, 2));
            //i0table[i] = gsl_sf_bessel_I0(facadj*rt)/val0;
            i0table[i] = bessi0(facadj*rt)/val0;
        }
        else
        {
            i0table[i] = 0.f;
        }
    }
}

dump_table()

std::vector<double> KaiserBessel::dump_table ( ) const

inline

Definition at line 174 of file xmipp_funcs.h.

    {
        return i0table;
    }

get_window_size()

int KaiserBessel::get_window_size ( ) const

inline

Return the size of the I0 selfWindow

Definition at line 197 of file xmipp_funcs.h.

    {
        return K;
    }

I0table_maxerror()

double KaiserBessel::I0table_maxerror

(

)

Compute the maximum error in the table

Definition at line 109 of file xmipp_funcs.cpp.

{
    double maxdiff = 0.f;
    for (int i = 1; i <= ntable; i++)
    {
        double diff = fabs(i0table[i] - i0table[i-1]);
        if (diff > maxdiff)
            maxdiff = diff;
    }
    return maxdiff;
}

i0win()

double KaiserBessel::i0win

(

double

x

)

const

Kaiser-Bessel I0 selfWindow function

Definition at line 71 of file xmipp_funcs.cpp.

{
    double val0 = double(bessi0(facadj));
    double absx = fabs(x);
    if (absx > vadjust)
        return 0.f;
    double rt = sqrt(1.f - pow(absx/vadjust, 2));
    double res = bessi0(facadj*rt)/val0;
    return res;
}

i0win_tab()

double KaiserBessel::i0win_tab ( double  x ) const

inline

Kaiser-Bessel I0 selfWindow function (uses table lookup)

Definition at line 186 of file xmipp_funcs.h.

    {
        double xt;
        if(x<0.)
            xt = -x*fltb+0.5;
        else
            xt = x*fltb+0.5;
        return i0table[ (int) xt];
    }

sinhwin()

double KaiserBessel::sinhwin

(

double

x

)

const

Kaiser-Bessel Sinh selfWindow function

Definition at line 122 of file xmipp_funcs.cpp.

{
    double val0 = sinh(fac)/fac;
    double absx = fabs(x);
    if (0.0 == x)
    {
        double res = 1.0f;
        return res;
    }
    else if (absx == alphar)
    {
        return 1.0f/val0;
    }
    else if (absx < alphar)
    {
        double rt = sqrt(1.0f - pow((x/alphar), 2));
        double facrt = fac*rt;
        double res = (sinh(facrt)/facrt)/val0;
        return res;
    }
    else
    {
        double rt = sqrt(pow((x/alphar),2) - 1.f);
        double facrt = fac*rt;
        double res = (sin(facrt)/facrt)/val0;
        return res;
    }
}

Member Data Documentation

alpha

double KaiserBessel::alpha

protected

Definition at line 152 of file xmipp_funcs.h.

alphar

double KaiserBessel::alphar

protected

table spastd::cing

Definition at line 159 of file xmipp_funcs.h.

dtable

double KaiserBessel::dtable

protected

Definition at line 158 of file xmipp_funcs.h.

fac

double KaiserBessel::fac

protected

alpha*r

Definition at line 160 of file xmipp_funcs.h.

facadj

double KaiserBessel::facadj

protected

Definition at line 162 of file xmipp_funcs.h.

fltb

double KaiserBessel::fltb

protected

Tabulate I0 selfWindow for speed

Definition at line 164 of file xmipp_funcs.h.

i0table

std::vector<double> KaiserBessel::i0table

protected

Definition at line 157 of file xmipp_funcs.h.

K

int KaiserBessel::K

protected

size in Ix-space

Definition at line 154 of file xmipp_funcs.h.

N

int KaiserBessel::N

protected

Kaiser-Bessel parameters

Definition at line 153 of file xmipp_funcs.h.

ntable

int KaiserBessel::ntable

protected

table I0 non-zero domain maximum

Definition at line 156 of file xmipp_funcs.h.

r

double KaiserBessel::r

protected

Definition at line 152 of file xmipp_funcs.h.

v

double KaiserBessel::v

protected

Definition at line 152 of file xmipp_funcs.h.

vadjust

double KaiserBessel::vadjust

protected

2*pi*alpha*r*v

Definition at line 161 of file xmipp_funcs.h.

vtable

double KaiserBessel::vtable

protected

I0 selfWindow size

Definition at line 155 of file xmipp_funcs.h.

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The documentation for this class was generated from the following files:

• xmippCore/core/xmipp_funcs.h
• xmippCore/core/xmipp_funcs.cpp