### abstract

- Equation (1) is periodic with respect to the spatial frequency with a period that is twice smaller than that in Eq.(6) in Ref. 1. Therefore, using the arguments in Ref. 1, a sampling condition that is twice more relaxed than that presented in Ref. 1 can be obtained; the sampling rate (1/) must be at least twice larger than the maximum local bandwidth (MLB). However as the example in Ref. 1 demonstrates, signals sampled at sampling rates lower than twice the MLB can be reconstructed (eg, 1/1.1 MLB in Fig. 4 in Ref. 1). Indeed, in Ref. 2 we prove that the sampling rate must be larger than the MLB as stated in Theorem 2 in Ref. 1, thus validating all the results of Ref. 1.