Detecting lines with houghlines in matlab
The biggest issue is that the pixels for each line are too few (I will explain with more details below). I would consider to stretch, and then dilate your raw image a little bit:
file='http://i.stack.imgur.com/LmIJJ.png';
I=imread(file);
I=imcrop(I,[1 206 size(I,2) size(I,1)]);
I=imresize(I,[size(I,1) 256]);
I=imdilate(I,strel('line',1,0));

I assume you are using the sample code from Mathworks on hough, houghlines, and houghpeaks. The problem is that there are not very many pixels along one slope in your image. You feel like it is a line, but it is actually a curve that consists of many short lines with different orientation. I think one parameter that you need to tune is the 'FillGap' which will connect the very short segments. I tried:
lines = houghlines(BW,T,R,P,'FillGap',30,'MinLength',15);

And the image I obtained:


There is still plenty of room for improvement, yet at least most lines are detected.
Note that the theta-axis in hough peaks indicates the slopes of the lines, you may also check them from lines, T, and R. But since the image has already been stretched along the 2nd dimension of raw data, you may need to scale them back (with some tangent transformations) if you plan to get the slopes of those detected lines.
Hope it helps, thank you.