The Set-Content cmdlet lets you write raw bytes to a file by using the Byte encoding:
$decoded = [System.Convert]::FromBase64CharArray($e, 0, $e.Length)
Set-Content out.png -Value $decoded -Encoding Byte
(However, BACON points out in a comment that Set-Content is slow: in a test, it took 10 seconds, and 360 MB of RAM, to write 10 MB of data. So, I recommend not using Set-Content if that’s too slow for your application.)