How do I make these properties that do the same thing DRY?

Question

My class has 3 properties that have to do the same thing in the custom set that I made. Now I have this repeated in all 3, which isn't DRY.

How do I make this DRY? Just put the foreach into a method? I feel like there must be a more elegant way.

(also I wish I didn't need the private backing fields because they are kind of an eye-sore)

private List<string> _ImageTypes;
public List<string> ImageTypes
{
    get { return _ImageTypes; }
    set
    {
        _ImageTypes = new List<string>();
        foreach (var type in value)
            if (!string.IsNullOrEmpty(type))
                _ImageTypes.Add("." + type.Replace(".", "").Replace("*", ""));
    }
}

private List<string> _AnimationTypes;
public List<string> AnimationTypes
{
    get { return _AnimationTypes; }
    set
    {
        _AnimationTypes = new List<string>();
        foreach (var type in value)
            if (!string.IsNullOrEmpty(type))
                _AnimationTypes.Add("." + type.Replace(".", "").Replace("*", ""));
    }
}

private List<string> _VideoTypes;
public List<string> VideoTypes
{
    get { return _VideoTypes; }
    set
    {
        _VideoTypes = new List<string>();
        foreach (var type in value)
            if (!string.IsNullOrEmpty(type))
                _VideoTypes.Add("." + type.Replace(".", "").Replace("*", ""));
    }
}

Answer 1

Yes, put it in the method

private List<string> CreateListFrom(List<string> list)
{
    return list.Where(type => !string.IsNullOrEmpty(type))
        .Select(type => type.Replace(".", "").Replace("*", ""))
        .Select(type => $".{type}")
        .ToList();
}

Then use it in the setters

private List<string> _ImageTypes;
public List<string> ImageTypes
{
    get { return _ImageTypes; }
    set
    {
        _ImageTypes = CreateListFrom(value);
    }
}

Another approach - do it in the constructor, then you can get rid of private members. But this will depend on how this class is consumed

Before talking about DRY - you should be sure that similar looking code are going to be changed for same reasons.