Line the base of a 20cm loose-bottomed round cake tin with greaseproof paper, if you wish. Melt the butter in a saucepan and stir in the crushed biscuits. Stir until well coated in the butter. Tip the biscuit mixture into the base of the prepared tin and spread out. Pack the biscuit crumb into the base with a spoon or a potato masher. Chill for 5 minutes.
Meanwhile, in a bowl mix together the cream cheese, Greek yogurt, double cream, lemon zest and juice and caster sugar. Fold in half the raspberries.
Remove the biscuit base from the fridge and spread the mixture over the biscuit base level the surface. Return to the fridge and and chill for at least 4 hours.
When ready to serve, remove the cheesecake from the fridge and dip a knife into hot water and dry it before running around the inside of the tin. Unclip the tin and lift the cheesecake out. Remove the greaseproof paper and serve decorated with the remaining raspberries and dust with icing sugar.