Java: reducing memory consumption by 2D float (floats[][]) arrays

I have Java application, which intensively working with 2D
float arrays (float[][] arrays), which actually holding images on black background. Both
dimensions are equals (square) and are power of 2 (mostly are 256, 512, 1024), so areas
close to borders have zeroes in most cases.

Having sizes equals to power of 2 done for
increasing performance (there is some FFT) and decreasing complexity on operations over
those arrays like rotation, etc.
Recently I faced lack of heap for this
application on my machine with 6Gb.
By my calculations - memory consumption
for this application should be like up to 2-3Gb, while it reaches 4-5Gb (looking in
Windows task manager).
I used "YourKit" profiler and it shows that those
floats arrays indeed takes most memory, however, total rough size for these floats
arrays should be like 1.3Gb (well, I know that it's up to JVM to decide how to store
data, but I was not expecting 2-3-times difference in memory
consumption).

I was trying to
compress/decompress data with Snappy compressor on the fly (and memory consumption drops
to 3.5Gb), but performance drops several times, which is not very
acceptable.
Also, I was testing performance when replacing those floats[][] by
BufferedImage, but performance was very
poor.

So, there is 2 ways left which
will work for me to decrease memory consumption:
1) write wrappers for
float[][] array in order to save on "zeroes" elements (there are a lot "empty" rows and
columns)
2) go away from "power of
2"

Both ways require quite a lot of
coding/refactoring, so while I am thinking "to be or not to be" - may be you have better
clue on this issue,
guys?

Thanks!