Make array from categories in woo

<?php
/**
 * My Setting class
**/
    if ( ! class_exists( 'WC_my_setting' ) ) {

        class WC_my_setting {

            public function __construct() {

                add_action( 'wp_enqueue_scripts', array( $this, 'setup_styles' ) ); // Enqueue the styles
                add_action( 'woocommerce_before_shop_loop_item_title', array( $this, 'woocommerce_do_something_on_frontend' ), 30 );

                // --------------------------------------------------------------------
                // Not sure where to place this code to pull in product categories needed
                // --------------------------------------------------------------------

                $categories =  $product->get_categories();
                if ( $categories ) {
                  foreach ( $categories as $cat ) {
                    $category_options[ $cat->slug ] = $cat->name;
                  }
                }

                // --------------------------------------------------------------------
                // This is how I need the array formatted
                // --------------------------------------------------------------------

                // $category_options = array(
                // 'clothing' => __( 'Clothing', 'woocommerce' ),
                // 'hoodies' => __( 'Hoodies', 'woocommerce' ),
                // 't-shirts' => __( 'T-shirts', 'woocommerce' ),
                // 'music' => __( 'Music', 'woocommerce' ),
                // 'albums' => __( 'Albums', 'woocommerce' ),
                // 'singles' => __( 'Singles', 'woocommerce' ),
                // 'posters' => __( 'Posters', 'woocommerce' ),
                // );

                // Init settings
                $this->settings = array(
                    array(
                        'name' => __( 'My Setting', 'woocommerce-my-setting' ),
                        'type' => 'title',
                        'id' => 'wc_my_setting_options'
                    ),
                    array(
                        'name'      => __( 'Name', 'woocommerce-my-setting'' ),
                        'desc'      => '',
                        'id'        => 'wc_my_setting_category',
                        'type'      => 'multiselect',
                        'options'   => $category_options
                    ),

                    array( 'type' => 'sectionend', 'id' => 'woocommerce-my-setting' ),
                );


                // Default options
                add_option( 'wc_my_setting_category', '' );


                // Admin
                add_action( 'woocommerce_settings_image_options_after', array( $this, 'admin_settings' ), 20 );
                add_action( 'woocommerce_update_options_catalog', array( $this, 'save_admin_settings' ) );
                add_action( 'woocommerce_update_options_products', array( $this, 'save_admin_settings' ) );
            }

                    /*-----------------------------------------------------------------------------------*/
            /* Class Functions */
            /*-----------------------------------------------------------------------------------*/

            // Load the settings
            function admin_settings() {
                woocommerce_admin_fields( $this->settings );
            }


            // Save the settings
            function save_admin_settings() {
                woocommerce_update_options( $this->settings );
            }


            // Setup styles
            function setup_styles() {
                if ( apply_filters( 'woocommerce_enqueue_styles', true ) ) {
                    wp_enqueue_style( 'wc-my-setting-styles', plugins_url( '/assets/css/style.css', __FILE__ ) );
                }
            }

        }

        $WC_nb = new WC_my_setting();
    }
}
?>