options(warn=-1) # turns off warnings, to turn on: "options(warn=0)"


library(imager)
library(png)

for (f in list.files(path="nt_toolbox/toolbox_general/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_general/", f, sep=""))
}

for (f in list.files(path="nt_toolbox/toolbox_signal/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_signal/", f, sep=""))
}

source("nt_toolbox/toolbox_wavelet_meshes/meshgrid.R")
options(repr.plot.width=3.5, repr.plot.height=3.5)

n <- 256
N <- n**2

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

options(repr.plot.width=4, repr.plot.height=4)

imageplot(x0)

sigma <- 0.08

y <- x0 + sigma*as.cimg(rnorm(N))

options(repr.plot.width=4, repr.plot.height=4)

imageplot(clamp(y))

cconv <- function(a, b){
    c <- fft(a)*fft(b)
    return( Re(fft(c, inverse=T )/length(c)) ) }

normalize <- function(h){ h/sum(as.vector(h)) }
t <- t( c(0:(n/2 - 1), -(n/2):(-1)) )
Y <- meshgrid_2d(t, t)$X ; X <- meshgrid_2d(t, t)$Y
h <- function(mu){ normalize(exp(-(X**2 + Y**2)/ (2*mu**2))) }

options(repr.plot.width=8, repr.plot.height=4)

mu <- 10
imageplot(fftshift_2d(h(mu)), 'h', c(1,2,1))
imageplot(fftshift_2d(Re(fft(h(mu)))), 'h_hat', c(1,2,2))

options(repr.plot.width=4, repr.plot.height=4)

imageplot(h(mu))

denoise <- function(x,mu){ cconv(h(mu), x) }

options(repr.plot.width=4, repr.plot.height=4)

imageplot(denoise(as.matrix(y), mu))

options(repr.plot.width=6, repr.plot.height=6)

source("nt_solutions/denoisingsimp_2b_linear_image/exo1.R")

options(repr.plot.width=6, repr.plot.height=4)

source("nt_solutions/denoisingsimp_2b_linear_image/exo2.R")

options(repr.plot.width=4, repr.plot.height=4)

imageplot(denoise(as.matrix(y), mu))

P <- as.matrix( (1/N) * ( abs(fft(x0))**2 ) )

h_w <- Re( fft(P / (P + sigma**2), inverse=T) / length(P) )

options(repr.plot.width=4, repr.plot.height=4)

u <- fftshift_2d(h_w)
imageplot( u[(n/2-9):(n/2+10),(n/2-9):(n/2+10)] )

options(repr.plot.width=4, repr.plot.height=4)

imageplot( cconv(as.matrix(y),as.matrix(h_w)) )
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