Convert a string with '\b' escape character (backspace) to a normal string

My string:

std::string With_esc = "asd\b";

I want to convert it to a simple string "as" (apply the backspace character and forget it). Is there any way to do this in C++? It should look like this:

std::string With_esc = "asd\b";
std::string Without_esc = With_esc; //Here I should convert it
std::ofstream FWith_esc ("with");
std::ofstream FWithout_esc ("without");
FWithout_esc << Without_esc;
FWith_esc << With_esc;

Bash:

~ cat -e with
  asd^H
~ cat -e without
  as

Unfortunately I don't know how to convert it, so both files look exactly the same.

Solution

Assuming you're lucky enough to use C++11 (otherwise adapt this code to your favorite regex engine):

string With_esc = R"asd\b";
string Without_esc = regex_replace(With_esc, regex(".\\b"), "");

As pointed out in comments this approach has following limitations:

It'll replace only one "back" so if you have "12\b\b" you'll get "1\b". To handle this you need to loop until input and output (for regex_replace()) are different (or maybe a better regex, I'm not such good with them).
It won't handle \b as beginning of the string like in "\b123". To handle this you need a simple string replacement (using technique suggested by Giobunny) to remove \b after a regex_replace().
Note here I'm using verbatim strings (it's ok for an example if your text comes from a file but if you're working with string literals you need to update regex accordingly).

UPDATE
As noted by Eric Finn this expression will also match multiple backspaces then "a\b\b\b" will become "\b\b" and then "\", that's obviously wrong. As he suggested a better regex should include check for "[^\b]\b" too.