Uncompressed format to PNG

The reason the FLAC is larger than the MP3 of the same data is because they encode differently. :) MP3 just encodes perceptual information, while FLAC stores every single speck of data, just in a more compact format.

• Converting a WAV to a FLAC is like converting a BMP to a PNG.
  • Same exact pixels, but compressed losslessly like a ZIP file into a smaller size.
• Converting a WAV to an MP3 is like converting a BMP to a JPEG.
  • Instead of storing exact pixels, it's really storing instructions for generating squares with ripples of color that look kind of like the original.

Similarly, MP3 just stores instructions for generating ripples that, when added together, sound kind of like the original. But the difference between the true signal and the generated signal (the error signal) consists of random noisy artifacts, like JPEG jaggies. When you then store this in a perfectionist format like FLAC, it needs to store all those jaggies, and random noise is harder to compress losslessly, so it increases the size of the file. (Truly random noise is incompressible. When you compress a file losslessly, you're eliminating redundant repeating patterns and making it look more like random noise.)

I bet if you convert the JPEG to PNG you will see the same kind of increase in size as you see when converting MP3 to FLAC, since the perfectionist lossless codec needs to remember every little jaggy and artifact that wasn't in the original bmp.

This analogy isn't perfect, since audio is more like a photo than a line-art diagram, but it helps get the idea across:

Original BMP size: 29 kB

PNG size: 629 B

JPEG size: 1.7 kB

PNG created from JPEG: 6.2 kB

To address your second question:

How to detect conversion from a lossy format like JPEG to TIFF or PNG

A visual way to tell if an image has been previously JPEG compressed is to zoom in on the image and look for signs of discontinuities between 8x8 pixel blocks. These are particularly obvious if the JPEG compression was high (low quality).

Low quality / High compression JPEG saved as PNG - 8x8 pixel blocks are clearly visible

But if the JPEG compression was low (high quality) then these blocks may be difficult to see...

High quality / Low compression JPEG saved as PNG - 8x8 pixel blocks are difficult to identify

So how to tell if this high quality image has been JPEG compressed at some point? JPEG compression deliberately drops more color information than intensity information and we can use Photoshop's Lab color mode to investigate further.

Convert your image to Lab color mode (Image -> Mode -> Lab Color). This converts the image from red, green and blue channels to L, a and b channels.

The L channel is the Lightness channel, essentially the greyscale version of the original image. The a and b channels are the color channels, but not in the traditional sense. A full explanation is not required for this answer but you can find more info on Wikipedia.

Inspect the a or b channel and look for 8x8 pixel blockiness.

'a' channel of previous image - 8x8 pixel blockiness visible, indicating JPEG compression

If either the a or b channels exhibit 8x8 pixel blockiness then that's a very good indication that the image was JPEG compressed at some point in the past.