Do you have Photoshop? If so, just do it there. AI is far from ideal for warping and distorting pixel images.
Presuming the image itself is undistorted as shown, you may:
1) Create a rectangle with the corners at the desired warped corners over the locked image;
2) Create the warped shape, possibly using narrow rectangles cut out from other rectangles with the Subtract from Shape Area/Minus Front, or rectangles made with the Grid Tool and Pathfinder>Divide (negative offset to separate resulting small rectangles), followed by an Effect>Warp>Bulge with negative horizontal value and Object>Expand Appearance, or other way;
3) Object>Clipping Mask>Make.
Jacob is correct this might be easier to make in Illustrtor than Photshop.
To make the grid of rectangles
1 Draw the rectangle
2 Object>Path>Split into Grid
3 Then make you Clipping Mask
This had to be edited. I took another look at your example and the grid has to be make with no space between the rows and columns,
Then the clipping maks
then you have to expand
then you have draw a larger rectangle with no fill and stroke to the width and height of the final art and then distribute the rectangles.
This is because in your example the image was exploded.
Then you can apply the warp.
You copy that art BTW to make the reflection and apply the arc warp and eliminate two rows give it some transparency.
Either make and opacity mask filled with a gradient or
fill the group with a gradient.
One more thig this is probably actually better done with the envelope distort make with mesh than the bulge. unless you want the rectangles curved
you also have to grout the rectangles after the split to grid.
Well I am going to offer a better way
after making the grid and clipping mask
use the free distort tool to make the perspective effect on the two sections on either end and then resize the center to accordingly.
like such takes about fifteen seconds.
If you need a video I will do one. Don't make the same mistake I made and turn off scale stroke and effects.
Thanks so much for your help!
I have plenty of detailed steps to give it a try.
For my part you are welcome, cpk3. It would be nice to see the outcome.