How can I create special search with check/uncheck image field in filter criteria of views
You will need BEF module to get exactly what you want, but it's not ready yet.

The workaround:
Although Drupal still has a query checkbox value bug (pretty ugly:(), there is a workaround and you can come up with the following close solution: 


Create a new filter criteria
Choose your image field "target_id" property. 
Configuring the filtering critera check "Expose this filter to visitors"
Choose "Grouped filters"
Mark "Optional" checkbox.
Widget type: radios.
Allow multiple selections.
Mark the first grouping (Grouping 1), give it a label and choose operator "Is not empty(NOT NULL).


You are now half way through. Altough it's working like this in view preview mode, it won't on the real page (because of the bug above). 

Now you need to write a hook_form_FORM_ID_alter in one of your .module file, mine's looks like this:

function base_form_views_exposed_form_alter(&amp;$form, \Drupal\Core\Form\FormStateInterface $form_state, $form_id) {
  if ($form['#id'] == 'views-exposed-form-search-page-1') {
    $request = \Drupal::requestStack()-&gt;getCurrentRequest()-&gt;query-&gt;all();
    $filter_identifier = 'field_image_target_id';
    if (!$request[$filter_identifier]) {
      $user_input = $form_state-&gt;getUserInput();
      unset($user_input[$filter_identifier]);
      $form_state-&gt;setUserInput($user_input);
    }
  }
}


WHERE: 

"views_exposed_form" => form_id (you will get the same, but check it)
"views-exposed-form-search-page-1" => is the '#id' parameter of your form. (this will be probably different)
"field_image_target_id" => This is your filter identifier, which can be found (also renamed) in when clicking on views this filter criteria.