Initiate a field in the storage of a contract with the source address of origination

I have the following smart contract where I pass admin address in the init function of the smart contract: (you can run it on smartPy online editor)

class SC(sp.Contract):
    def __init__(self, admin):
        self.init(administrator = admin, value = 0)


    @sp.entry_point
    def increment(self, params):
        sp.verify(sp.sender == self.data.administrator)
        self.data.value =+ 1

if "templates" not in __name__:
    @sp.add_test(name = "SC")
    def test():

        scenario = sp.test_scenario()
        scenario.h1("SC")

        admin = sp.address("tz1-admin-address-1234")
        alice = sp.address("tz1-alice-address-1234")

        c1 = SC(admin)

        scenario += c1
        scenario.h2("Admin increments value")
        scenario += c1.increment().run(sender = admin)
        scenario.h2("Alice tries to increment value")
        scenario += c1.increment().run(sender = alice, valid = False)

        scenario.verify(c1.data.value == 1)

Can I initiate the administrator field in storage by doing something like:

class SC(sp.Contract):
    # admin is no longer passed here
    def __init__(self): 
        # Difference here
        self.init(administrator = sp.source, value = 0)


    @sp.entry_point
    def increment(self, params):
        sp.verify(sp.sender == self.data.administrator)
        self.data.value =+ 1

if "templates" not in __name__:
    @sp.add_test(name = "SC")
    def test():

        scenario = sp.test_scenario()
        scenario.h1("SC")

        admin = sp.address("tz1-admin-address-1234")
        alice = sp.address("tz1-alice-address-1234")

        # Difference here
        c1 = SC().run(source = admin) # or c1 = SC()

        scenario += c1
        scenario.h2("Admin increments value")
        scenario += c1.increment().run(sender = admin)
        scenario.h2("Alice tries to increment value")
        scenario += c1.increment().run(sender = alice, valid = False)

        scenario.verify(c1.data.value == 1)

What I want is initiate the administrator without passing his address in the init when deploying but by setting the deployer (source of the origination) as administrator.

Thank you in advance.