There is a constant set in functions.php that determines the size of the header image, which I take it is what you are referring to. The fuzziness would be because of the resizing upwards.
Here’s the code(with comments and white space removed to save space) :
if ( ! brunelleschi_option('content-width') ) { $content_width = 960; }
else { $content_width = brunelleschi_option('content-width'); }
if(brunelleschi_option('use-header-image')) {
if ( ! defined( 'HEADER_IMAGE' ) ) { define( 'HEADER_IMAGE', '%s/images/headers/beach.png' ); }
define( 'HEADER_IMAGE_WIDTH', apply_filters( 'brunelleschi_header_image_width', $content_width ) );
define( 'HEADER_IMAGE_HEIGHT', apply_filters( 'brunelleschi_header_image_height', 198 ) );
...
So it looks as though the theme allows you to change the content width, in which case, the header image width is reduced to suit the content width. The height is set to 198 (pixels, presumably).
If I have it right, I guess you could do something like:
if(brunelleschi_option('use-header-image')) {
if ( ! defined( 'HEADER_IMAGE' ) ) { define( 'HEADER_IMAGE', '%s/images/headers/beach.png' ); }
define( 'HEADER_IMAGE_WIDTH', 430 );
define( 'HEADER_IMAGE_HEIGHT', apply_filters( 'brunelleschi_header_image_height', 88 ) );
...
You would then have to see how this looked and alter your CSS to get the image positioned correctly, I would think.
I would recommend strongly that you keep a backup of the original functions.php file before you make any changes. Normally, I’d recommend doing this sort of thing in a child theme, but in this case I don’t see how that would work, given that the code above is not contained within a function. If I understand things correctly, this means that the code above would run after anything you put in a child theme.
Alternatively, you could try modifying the header.php file, preferably in a child theme, replacing the references to the constants HEADER_IMAGE_HEIGHT and HEADER_IMAGE_WIDTH with literal values.
HTH
PAE