Hi,
I know that there is a possibility that we could find some articles on the internet with this thematic, but let me add my own version.

Programmatic Un-Canceling orders should not be the best way to resolve the issues with an order canceled by mistake.

It is more recommended to re-create the order from the admin instead (if possible). But there are some specific situations in which we really need to do this, so let’s get to the code:

//...
 
$order = Mage::getModel('sales/order')->loadByIncrementId($incrementId);
 
$order->setSubtotalCanceled(null);
$order->setBaseSubtotalCanceled(null);
 
$order->setTaxCanceled(null);
$order->setBaseTaxCanceled(null);
 
$order->setShippingCanceled(null);
$order->setBaseShippingCanceled(null);
 
$order->setDiscountCanceled(null);
$order->setBaseDiscountCanceled(null);
 
$order->setTotalCanceled(null);
$order->setBaseTotalCanceled(null);
 
$order->setState(Mage_Sales_Model_Order::STATE_PENDING_PAYMENT, 
 'pending_payment', 'This order is uncanceled by Admin!');
 
$order->setStatus(Mage_Sales_Model_Order::STATE_PENDING_PAYMENT);
$order->save(); 
 
//Don't forget to un-cancel order items ...
foreach ($order->getAllItems() as $item) {
 $item->setQtyCanceled(0);
 $item->save();
} 
 
//...