Ygtjki

I need to add axes to a bunch of figures in my document, I'm trying with tikz but maybe there's an easier and more elegant way to do it (looking at you, overpic)?
The result I'm trying to achieve is not like this, I need the axes to have the arrows as well.

I got some MWE working, but the axes are vertically misaligned (they should be outside of the picture). I've tryed adding vspaces but they don't seem to work as I'd like.

Thanks in advance for your help!

MWE:

documentclassscrreprt
usepackagesubfig
usepackagegraphicx
usepackagetikz
begindocument
 beginfigure[h!]
 vspace-0.6cm
 centering
 subfloat[]%
 begintikzpicture
 draw [->] (0,0) -- (0.5,0) node[right]footnotesize(y);
 draw [->] (0,0) -- (0,0.5) node[above]footnotesize(x);
 endtikzpicture
 hspace-1cm
 includegraphics[width=0.45textwidth,height=1cm]example-image-a
 quad
 subfloat[]%
 begintikzpicture
 draw [->] (0,0) -- (0.5,0) node[right]footnotesize(y);
 draw [->] (0,0) -- (0,0.5) node[above]footnotesize(x);
 endtikzpicture
 hspace-1cm
 includegraphics[width=0.45textwidth,height=1cm]example-image-a
 \
 subfloat[]%
 includegraphics[width=0.45textwidth,height=1cm]example-image-a
 hspace-0.9cm
 begintikzpicture
 draw [->] (0,0) -- (-0.5,0) node[left]footnotesize(y);
 draw [->] (0,0) -- (0,0.5) node[above]footnotesize(x);
 endtikzpicture
 quad
 subfloat[]%
 includegraphics[width=0.45textwidth,height=1cm]example-image-a
 hspace-0.9cm
 begintikzpicture
 draw [->] (0,0) -- (-0.5,0) node[left]footnotesize(y);
 draw [->] (0,0) -- (0,0.5) node[above]footnotesize(x);
 endtikzpicture
 captionFoo
 endfigure
enddocument

EDIT I would like the axes to be something like this:

If you don't want to use the heavy tikz weapons, picture mode is sufficient to draw a few arrows:

documentclassscrreprt
usepackagesubfig
usepackagegraphicx
%usepackagetikz
begindocument
 beginfigure[htbp]
 vspace-0.6cm
 centering
 subfloat[]%
 setlengthunitlengthtextwidth
 beginpicture(.45,0.1)
 put(0,0)includegraphics[width=0.45textwidth,height=1cm]example-image-a
 put(.46,-.01)vector(-1,0).07
 put(.46,-.01)vector(0,1).05
 put(.453,.045)x
 put(.373,-.014)y
 endpicture
 
 captionFoo
 endfigure
enddocument

Second approach with the heavy tikz weapons:

documentclassscrreprt
usepackagesubfig
usepackagegraphicx
usepackagetikz
begindocument
 beginfigure[htbp]
 vspace-0.6cm
 centering
 subfloat[]%
 begintikzpicture
 node (image) at (0,0) includegraphics[width=0.45textwidth,height=1cm]example-image-a;
 draw [->] (image.south west) -- ++(0.5,0) node[right]footnotesizetextity;
 draw [->] (image.south west) -- ++(0,0.5) node[above]footnotesizetextitx;
 endtikzpicture
 
 endfigure
enddocument

Off-topic: I would not use [h!] as floating specifier, this is almost always a guarantee for bad image placement

Maybe like this?

documentclassarticle
begindocument
<<test,echo=F,fig.cap="Axis with background image and more.">>=
library(png)
ima <- readPNG("/usr/local/texlive/2018/texmf-dist/tex/latex/mwe/example-image-a.png")
plot(1:2, type='n', xlab="x", ylab="y",xlim=c(0,10),ylim=c(0,7.5),axes=F)
lim <- par()
u <- par("usr") 
rasterImage(ima, u[1]+.5, u[3]+.5, u[2]-.5, u[4]-.5)
arrows(u[1], u[3], u[2], u[3], code = 2, xpd = TRUE) 
arrows(u[1], u[3], u[1], u[4], code = 2, xpd = TRUE)
lines(c(1, 1.2, 1.35,4.5, 6, 8.3, 9.5), c(.6, 1.3, 0.9,2.7, 0.6, 4.7, 7.0), lwd=5, col="blue")
@
enddocument

Of course, this need R and knitr to be compiled.

If you need only a little axis:

documentclassarticle
begindocument
<<test,echo=F,fig.cap="Axis with background image and more.">>=
library(png)
ima <- readPNG("/usr/local/texlive/2018/texmf-dist/tex/latex/mwe/example-image-a.png")
plot(1:2, type='n', xlab="", ylab="",xlim=c(0,10),ylim=c(0,7.5),axes=F)
lim <- par()
u <- par("usr") 
rasterImage(ima, u[1]+.5, u[3]+.5, u[2]-.5, u[4]-.5)
arrows(u[1], u[3], u[2]/3, u[3], code = 2, xpd = TRUE) 
arrows(u[1], u[3], u[1], u[4]/3, code = 2, xpd = TRUE)
axis(1, at=u[2]/6, tck=0, labels="x") 
axis(2, at=u[4]/6, tck=0, labels="y") 
lines(c(1, 1.2, 1.35,4.5, 6, 8.3, 9.5), c(.6, 1.3, 0.9,2.7, 0.6, 4.7, 7.0), lwd=5, col="blue")
@
enddocument