I solved the issue. It was my mistake. Here is the solution:
<label>
<input type="radio" name="<?php echo esc_attr($field['name']); ?>" value="1" <?php checked( $field['value'], 1 ); ?> />
<img src="<?php echo get_template_directory_uri(); ?>/admin/layout-1.png">
</label>
<label>
<input type="radio" name="<?php echo esc_attr($field['name']); ?>" value="2" <?php checked( $field['value'], 2 ); ?> />
<img src="<?php echo get_template_directory_uri(); ?>/admin/layout-1.png">
</label>
<label>
<input type="radio" name="<?php echo esc_attr($field['name']); ?>" value="3" <?php checked( $field['value'], 3 ); ?> />
<img src="<?php echo get_template_directory_uri(); ?>/admin/layout-1.png">
</label>