from __future__ import division
from nt_toolbox.general import *
from nt_toolbox.signal import *
%pylab inline
%matplotlib inline
%load_ext autoreload
%autoreload 2

n = 256
N = n**2

name = 'nt_toolbox/data/flowers.png'
x0 = load_image(name, n)

imageplot(x0)

sigma = .08

y = x0 + sigma*random.standard_normal(x0.shape)

imageplot(clamp(y))

cconv = lambda a,b : real(ifft2(fft2(a)*fft2(b)))

normalize = lambda h : h/sum(h.flatten())
t = transpose( concatenate( (arange(0,n/2), arange(-n/2,0) ) ) )
[Y,X] = meshgrid(t, t)
h = lambda mu: normalize(exp(-(X**2 + Y**2)/ (2*mu**2)))

mu = 10
subplot(1,2, 1)
imageplot(fftshift(h(mu)))
title('h')
subplot(1,2, 2)
imageplot(fftshift(real(fft2(h(mu)))))
title('$\hat h$');

imageplot(h(mu))

denoise = lambda x,mu : cconv(h(mu), x)

imageplot(denoise(y, mu))

run -i nt_solutions/denoisingsimp_2b_linear_image/exo1

run -i nt_solutions/denoisingsimp_2b_linear_image/exo2

imageplot(denoise(y, mu))

P = 1/N * ( abs(fft2(x0))**2 )

h_w = real(ifft2(P / (P + sigma**2)))

u = fftshift(h_w)
imageplot( u[n/2-10:n/2+10,n/2-10:n/2+10] )

imageplot( cconv(y,h_w) )