i am scientist and i have data filled with "noise". data is such for x=1 there are set of values of y e.g. for x=1 y belongs to {1,4,6,7,9,18,16,19} and i have 100 such sets each for there respected x values e.g. for x=2 y belongs to{1,5,7,4} for x=3 y belongs to {2,6,4,8,2}....for x=100 y belongs to {2,7,89,4,5} now i want to choose single value from each set of y so that this 100 values together will fit in sinusoidal curve, unfortunately whose parameters are unknown. in other language i have data for x values from 1 to 100, for each x value only one 'y' value is real rest are noise and all this 100 real values of y are in sinusoidal pattern , is any optimization algorithm exist for this?

Your data is your data. Sometimes you get noisy data and sometimes not as noisy. You can't just discard data you don't like.

unfortunately there is no way of determining the right value. you'll just have to do a curve fitting