Function Definition:

function RemoveDuplicateItems(items, propertyName) {
    var result = [];
    if (items.length > 0) {
        $.each(items, function (index, item) {
            if ($.inArray(item[propertyName], result) == -1) {
                result.push(item);
            }
        });
    }
    return result;
}

Function Usage:
In the below code, assumption is that, the REST call returns data.d.results and the column for which duplicate items need to be removed is Title

var items = data.d.results;
items = RemoveDuplicateItems(items, 'Title');

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