The best way you can do for both Html.ActionLink and Ajax.ActionLink is as below
@Html.Raw(@Html.ActionLink("[replacetext]", "Index", "Home").ToHtmlString().Replace("[replacetext]", "<img src=\"/Content/img/logo.png\" ... />"))
@Html.Raw(@Ajax.ActionLink("[replacetext]", "Index", "Home", new AjaxOptions { UpdateTargetId="dvTest"}).ToHtmlString().Replace("[replacetext]", "<img src=\"/Contents/img/logo.png\" … />"))
additionaly you want to provide class and style so you can do as following
@Html.Raw(@Ajax.ActionLink("[replacetext]", "Index", "Home", new AjaxOptions { UpdateTargetId="dvTest"}).ToHtmlString().Replace("[replacetext]", "<img src=\"/Contents/img/logo.png\" style=\"width:10%\" … />"))