Files uploaded via the field widget Image will result in a failure

I think you should post more info, storage configuration , field setting etc.

It may not be an error specific to storage.
When I try to upload images that are larger than 425Kb, I get this message:

An AJAX HTTP request terminated abnormally.
Debugging information follows.
Path: /?q=file/ajax/field_image/und/0/form-_JAuwwO_y4sqBl5hsun2cppYB_qPq7Ck29femzSQDM0
StatusText: n/a
ResponseText: 

There seems to be quite a few people getting this Ajax error but as yet I haven't seen a solution.

My particular issue with file uploads was resolved by my host increasing the delay before timeout
ie in php.ini

max_execution_time = 60

A low network between ftp server and web server?

I encountered similar Ajax error message as well on an Image field.
The error only occur when the field has "Preview image style" turned on.
In my case, I get it working with either these solutions:

1. Turn off the preview.
Go to 'Manage Fields', click on edit of the field. Under "Preview image style", select " < no preview > ".

2. Patch the code on storage_core_bridge.module.
The issue is coming from DrupalStorageStreamWrapper->getExternalUrl().
The nested "try catch" is not catching StorageException thrown by Storage->construct() -- storage.inc line 19.
I've updated my storage_core_bridge.module to the following:

public function getExternalUrl() {
   try {
        $storage = storage_core_bridge_load($this->uri);
      }
      catch (StorageException $e) {
         // We couldn't find the storage - maybe it's a styled image that hasn't been created yet.
        try {
          $storage = storage_core_bridge_styled_image_create($this->uri);
        }
        catch (StorageException $e) {
          return FALSE;
        }
      }
      return $storage->serveURL(TRUE);  
 }

If still an issue please reopen this ticket and we will take a look at it!