How to reconstruct an image from s-parameters in Matlab? I have a set of data which is the s-parameter (s11), consisting of 2 columns ($1001 \times 2$). The first column represents the frequency and the second column is the magnitude in dB. I need to use these data to reconstruct an image using Matlab but I have no idea how to do it. 

I know that I have to use ifft function first to transform from frequency domain to time domain but the result I had consists of real and imaginary part and I do not know how to deal with this.
Each complex value can be described as $$A \cdot e^{i\cdot \phi}  $$. 
Where A is the magnitude and $\phi$ the angle.
With this knowlege you can use the ifft as you allready mentioned. 
If you consider that the image is a real signal you can take the real part by using real(). 

So overall it the part after reading the magnitude and angle would look like 

IMG = uint8(real(ifft2(mag .* exp(i * angle)))); 


Where IMG is the resulting image, mag the array of magnitudes (in linear scaling), angle the array of angles.

The only problem with that is, that you have to know the dimensions of the image. The spectrum of an image has (after FFT) the same dimensions as the picture (113 x 200 pixel picture -> 113 x 200 matrix after FFT).
So your mag and angle must have the dimension of the resulting picture (e.g. 113 x 200).