How to remove header image in Twenty Eleven theme?

<?php 
// REMOVE TWENTY ELEVEN DEFAULT HEADER IMAGES
function wptips_remove_header_images() {
    unregister_default_headers( array('wheel','shore','trolley','pine-cone','chessboard','lanterns','willow','hanoi')
    );
}
add_action( 'after_setup_theme', 'wptips_remove_header_images', 11 );
?>

Use this code in you function.php file to remove header image.

Login to the admin, go to appearance then click on header link (will be shown if the theme is currently activated). After that click 'Remove Header Image' button there.

If you want to remove this in the code. Then, go to the theme folder, open header.php. Find and delete this code:

<?php
    // Check to see if the header image has been removed
    $header_image = get_header_image();
    if ( ! empty( $header_image ) ) :
?>
<a href="<?php echo esc_url( home_url( '/' ) ); ?>">
    <?php
        // The header image
        // Check if this is a post or page, if it has a thumbnail, and if it's a big one
        if ( is_singular() &&
                has_post_thumbnail( $post->ID ) &&
                ( /* $src, $width, $height */ $image = wp_get_attachment_image_src( get_post_thumbnail_id( $post->ID ), array( HEADER_IMAGE_WIDTH, HEADER_IMAGE_WIDTH ) ) ) &&
                $image[1] >= HEADER_IMAGE_WIDTH ) :
            // Houston, we have a new header image!
            echo get_the_post_thumbnail( $post->ID, 'post-thumbnail' );
        else : ?>
        <img src="<?php header_image(); ?>" width="<?php echo HEADER_IMAGE_WIDTH; ?>" height="<?php echo HEADER_IMAGE_HEIGHT; ?>" alt="" />
    <?php endif; // end check for featured image or standard header ?>
</a>
<?php endif; // end check for removed header image ?>

Hope it answers your question.