Currently sitecore is using the SelectMediaDialog component to display the values in the default view, this is defined in core database at
/sitecore/client/Applications/Dialogs/SelectMediaDialog. More info about the media search page components and how they are added https://doc.sitecore.com/developers/speak/90/speak/en/walkthrough--create-a-search-page.html
You could create a custom searchconfig similar to the existing navigation items which are defined under
/sitecore/client/Applications/Dialogs/SelectMediaDialog/PageSettings/Navigation/CatalogItems/Media and are referencing the configuration items defined
/sitecore/client/Applications/Dialogs/SelectMediaDialog/PageSettings/SearchConfigs, out of the box the component supports filtering by Root/Template/Base Templates and custom search.
The challenge would be identifying the media items that you need to show on the page, if they can share for example the same template, base template or field value then the out of the box filters should be sufficient. Otherwise it would need further customization or creating custom facets.
The SelectMediaDialog page is using as rendering the component
/sitecore/client/Business Component Library/version 1/Layouts/Renderings/Data/SearchDataSource and the SPEAK js file located