To get a list of lists of pixel values of that part of the image, you'd use the following. It's going to give results in the range [0,1].
ImageData@ImageTake[image,{1,1024},{1,371}]
You could use //MatrixForm at the end of that to get a giant matrix, but beware, it could be a little intensive to display a matrix that big. Like, crash-your-kernel intensive!
I'm not entirely sure what you mean by "Gaussian fitting with particles image", maybe you could clarify. But if you meant trying to find some linear transform that will make the image's histogram look vaguely gaussian, you could use this, where mu is the mean of your gaussian and sigma is the standard deviation.
i = ImageTake[image,{1,1024},{1,371}];
HistogramTransform[image,NormalDistribution[mu, sigma]]
Good luck!