In an imaging system, the sensor is only capable of recording the "phase" $($or angle:

$\{$:${}_x({}_1,{}_2))$ of the input image $($we mean; the angle of the Fourier transform, of course$).$

In fact, many infrared imaging systems work that way! Starting from this phase

information, and knowing the image size and the dynamic range of the image, we construct

the following iterative algorithm:

As you can see, there are three projection operations here. In the first, the Fourier

Transform of the image is forced to have the phase: $.$ In the second, The out$-$of$-$image$-$

bounds is set to zero value. In the third, The pixel values are forced to be between $0$ and

b$)$ Implement this algorithm with a Matlab program. Take a small $($like$,64$x$64)$

Matlab test image, and run your program. Take snapshots of your intermediate

results $($during various spteps of your iteratiob$)$ and put these results on your

exam paper as well as your program listing. As a suggestion, I recommend that,

if your image is $6464,$ the Fourier transform $($FFT$)$ size should better be taken

as at least $256256.$ Your submission must include initial, some intermediate,

and final recunstruction images, as well as the $".$m$"$ file script.