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      $arFilter = array(
         "IBLOCK_ID"=>$arParams["IBLOCK_ID"],
         "GLOBAL_ACTIVE"=>"Y",
         "IBLOCK_ACTIVE"=>"Y",
         "<="."DEPTH_LEVEL" => $arParams["DEPTH_LEVEL"],
         // Parameter added
         "CNT_ACTIVE" => "Y"
      );

/* remove empty sections ----------------------------------------*/
foreach ($arResult  as $key => $value) {
   if (preg_match('/\((\d+)\)/', $value['TEXT'], $matches)) {
      if (0 == $matches[1]) {
         unset($arResult[$key]);
      }
   }
}

if ($arResult['ITEMS'])

    foreach ($arResult['SECTIONS'] as $key => $value) {
        $arSelect = Array("ID");
        $sect = CIBlockElement::GetList(
            Array("ID" => "DESC"),
            Array("IBLOCK_ID" => #НОМЕР_ИНФОБЛОКА#,
                "ACTIVE" => "Y",
                "SECTION_ID" => Array($arResult['SECTIONS'][$key]['ID']),
                "INCLUDE_SUBSECTIONS" => 'Y',
                "CATALOG_AVAILABLE" => "Y"
            ),
            false,
            Array("nTopCount" => 3),
            $arSelect);

        $count = 0;
        while ($el = $sect->GetNextElement()) {
            $count++;
            if ($count > 1) break;
        };
        if ($count < 1) unset($arResult['SECTIONS'][$key]);

    }