I have tried several methods and found out that using cPickle with setting the protocol argument of the dumps method as: cPickle.dumps(obj, protocol=cPickle.HIGHEST_PROTOCOL) is the fastest dump method.
import msgpack
import json
import pickle
import timeit
import cPickle
import numpy as np
num_tests = 10
obj = np.random.normal(0.5, 1, [240, 320, 3])
command = 'pickle.dumps(obj)'
setup = 'from __main__ import pickle, obj'
result = timeit.timeit(command, setup=setup, number=num_tests)
print("pickle:  %f seconds" % result)
command = 'cPickle.dumps(obj)'
setup = 'from __main__ import cPickle, obj'
result = timeit.timeit(command, setup=setup, number=num_tests)
print("cPickle:   %f seconds" % result)
command = 'cPickle.dumps(obj, protocol=cPickle.HIGHEST_PROTOCOL)'
setup = 'from __main__ import cPickle, obj'
result = timeit.timeit(command, setup=setup, number=num_tests)
print("cPickle highest:   %f seconds" % result)
command = 'json.dumps(obj.tolist())'
setup = 'from __main__ import json, obj'
result = timeit.timeit(command, setup=setup, number=num_tests)
print("json:   %f seconds" % result)
command = 'msgpack.packb(obj.tolist())'
setup = 'from __main__ import msgpack, obj'
result = timeit.timeit(command, setup=setup, number=num_tests)
print("msgpack:   %f seconds" % result)
Output:
pickle         :   0.847938 seconds
cPickle        :   0.810384 seconds
cPickle highest:   0.004283 seconds
json           :   1.769215 seconds
msgpack        :   0.270886 seconds