Finding linear chirp parameters from a low quality spectrogram, possibly with image processing techniques?
I think you can use standart method of fitting data to Straight Line. See for example explanation in 15.2 of "Numerical Recipes in C" http://apps.nrbook.com/c/index.html (page 661-662)


To prepare arrays of $x_i$, $y_i$, $\sigma_i$, you must for each point on your image (frequency-time):
$x_i$ := frequency
$y_i$ := time
$\sigma_i$ := 1/intensity (or 1/intensity$^2$)
size of arrays will be N*M (N, M - x and y size of spectrogram in points)
Calculate a and  b (y = a + b*x) by using formula (15.2.6) from http://apps.nrbook.com/c/index.html
If it will be some problem with outliers, use some robust fitting method. See for example 15.7 of  http://apps.nrbook.com/c/index.html. But I think there will not such problem with your data.


This method is faster then Hough transform

EDIT
It is very important to choose good expression for $\sigma_i$. May be better results will be with $\sigma_i$ := $1/\sqrt{intensity}$. May be will be better to use $\sigma_i$ := 1/(intensity-background) for (intensity > background) and exclude all points with (intensity &lt; background). If there are some limitations on parameres of straight line (a,b), you can exclude some x-y points from $x_i$-$y_i$ arrays. But this modifications depend on actual data. It will be very interesting to see the your results.