Preheat the oven to 325°F/ 160°C and line muffin tins with paper cases. In a bowl mix the digestive biscuits, melted butter and sugar. Mix together with a fork until combined well and the mixture is crumblike. To make the raspberry purée, mix together the raspberries and sugar in a food processor. Blitz until smooth, and then sieve into a bowl to remove.
To make the cheesecake, mix together the cream cheese on medium-high speed in the bowl of an electric mixer until light and airy. Mix in the sugar until smooth. Blend in the salt and vanilla. Beat in the eggs gradually, mixing well before adding the next.
To make the cupcakes, add 3 tablespoons of the cheesecake batter over the base in each cupcake liner. Drop ½ teaspoon of raspberry puree lightly over the cheesecake filling. Use a knife to lightly swirl and create a marbled effect.
Bake in the oven until the cheesecake filling is set. This takes 20-22 minutes roughly, allow to cool in the oven before removing and then transfer to a wire rack. Take out of the tin and remove to the firdge to chill for a minimum of 4 hours.