Reducing the file size of a very large images, without changing the image dimensions

PNG is not a lossy image format, so you would likely need to convert the image into another format-- most likely JPEG. JPEG has a settable "quality" factor-- you could simply keep reducing the quality factor until you got an image that was small enough. All of this can be done without changing the image resolution.

Obviously, depending on the image, the loss of visual quality may be substantial. JPEG does best for "true life" images, such as pictures from cameras. It does not do as well for logos, screen shots, or other images with "sharp" transitions from light to dark. (PNG, on the other hand, has the opposite behavior-- it's best for logos, etc.)

However, at 800x600, it likely will be very easy to get a JPEG down under 1MB. (I would be very surprised to see a 30MB file at those smallish dimensions.) In fact, even uncompressed, the image would only be around 1.4MB:

800 pixels * 600 pixels * 3 Bytes / color = 1,440,000 Bytes = 1.4MB

Therefore, you only need a 1.4:1 compression ratio to get the image down to 1MB. Depending on the type of image, the PNG compression may very well provide that level of compression. If not, JPEG almost certainly could-- JPEG compression ratios on the order of 10:1 are not uncommon. Again, the quality / size of the output will depend on the type of image.

Finally, while I have not used ImageMagick in a little while, I'm almost certain there are options to re-compress an image using a specific quality factor. Read through the docs, and start experimenting!

EDIT: Looks like it should, indeed, be pretty easy with ImageMagick. From the docs:

$magick> convert input.png -quality 75 output.jpg

Just keep playing with the quality value until you get a suitable output.

Your example is troublesome because a 30MB image at 800x600 resolution is storing 500 bits per pixel. Clearly wildly unrealistic. Please give us real numbers.

Meanwhile, the "cheap and cheerful" approach I would try would be as follows: scale the image down by a factor of 6, then scale it back up by a factor of 6, then run it through PNG compression. If you get lucky, you'll reduce image size by a factor of 36. If you get unlucky the savings will be more like 6.

pngtopng big.png | pnmscale -reduce 6 | pnmscale 6 | pnmtopng > big.png

If that's not enough you can toss a ppmquant in the middle (on the small image) to reduce the number of colors. (The examples are netpbm/pbmplus, which I have always found easier to understand than ImageMagick.)

To know whether such a solution is reasonable, we have to know the true numbers of your problem.

Also, if you are really going to throw away the information permanently, you are almost certainly better off using JPEG compression, which is designed to lose information reasonably gracefully. Is there some reason JPEG is not appropriate for your application?

Since the size of an image file is directly related to the image dimensions and the number of colours, you seem to have only one choice: reduce the number of colours.

And ~30MB down to 1MB is a very large reduction.

It would be difficult to achieve this ratio with a conversion to monochrome.