I am not certain what you are wanting...
Image size reduction,
or an alpha transparency problem.
For the size reduction, the problem may be going from JPG to PNG. JPG is a lossy file format and as such it tends to generate extra colors, and '
ringing' effects (see
IM Examples, JPG lossy effects). This means the pixels in the generated JPG image are not very smooth, particularly for almost pure black and white images such as what your example shows. That in tern make compression a lot more difficult.
I sugget you filter the image though -normalize, or maybe -contrast-stretch 4% to try and remove the color noise, and then it should compress much better. Also run the result though optipng or pngquant (see
IM Examples, PNG Other Utilities
If it is a transparency problem, You will need to be more clear of exactly what you are trying to do.
For a gray-scale (mostly black and white image) in an PNG with black on transparent then I suggest using
-negate -background black -alpha shape to do the conversion. This uses the source gray-scale image as a transparency mask to generate a pure black 'shape' image, which is black on transparent!
For more info in 'shape' images see
Alpha shape and