simulPET/fisher1D.py

import numpy
import matplotlib.pyplot
import scipy.special

def generateAlgebra(w,o,bw,FWHM,R):
    sigma=FWHM/2.35
    ctr=0.5*o.size
    #w=numpy.zeros([n,n])
    q=bw/numpy.sqrt(2)
    for i in numpy.arange(o.size):
        for j in numpy.arange(o.size):
            w[i,j]=0.5*(scipy.special.erf(q*(j-i+0.5)/sigma)-
                scipy.special.erf(q*(j-i-0.5)/sigma))

    #o=numpy.zeros(n)
    p=0
    for i in numpy.arange(o.size):
        if numpy.abs(i-ctr)<R/bw:
            o[i]=1
            p+=1;
    o/=numpy.sqrt(p)


def SNR(o,w):
    return numpy.dot(numpy.dot(o,w),o)/\
            numpy.sqrt(numpy.dot(numpy.dot(numpy.dot(o,w),w),o))

def Noise(o,w):
    return numpy.sqrt(numpy.dot(numpy.dot(numpy.dot(o,w),w),o))

def Signal(o,w):
    return numpy.dot(numpy.dot(o,w),o)

def graphSNR(n,bw,x,R,var):
    s=numpy.zeros(x.size)
    w=numpy.zeros([n,n])
    o=numpy.zeros(n)
    for i in numpy.arange(x.size):
        generateAlgebra(w,o,bw,x[i],R)
        if var=="SNR":
            s[i]=SNR(o,w)
        if var=="Signal":
            s[i]=Signal(o,w)
        if var=="Noise":
            s[i]=Noise(o,w)
    return s