Receiver grouping is commonly used in marine towed-streamer seismic acquisition. Measurementsfrom several receivers in a group are stacked to increase the signal-to-noise ratio(S/N) of the resulting data and to form an analog spatial anti-aliasing filter. I propose amethod for extracting in-line derivatives of the wavefield as additional measurements fromthe groups. This is achieved by multiplying the signal from the individual receivers in agroup with predefined weights that corresponds to a finite-difference (FD) operator. Thein-line derivative(s) makes it possible to utilize multi-channel sampling theorems to reconstructthe signal on a denser grid. Extraction of finite differences from clusters of receiversis not a new concept, but I show that by using the geometry of conventional streamergroups it is possible to obtain finite difference data which are well-suited for multi-channelinterpolation. The key to finding suitable FD operators is to recognize that it is not theperfect differentiation response we seek, but the impulse response of the group multipliedwith the ideal differentiation response. Furthermore, under a Gaussian noise assumption, Iderive formulae for the resulting noise level from sinc and higher-order sinc interpolations.It is shown that the random noise level in the reconstructed data, when using higher-ordersinc interpolation, is expected to be higher than when using conventional sinc interpolation,and will vary with respect to the distance from the original sampling points. The statisticalanalysis shows that it is beneficial to find FD operators with as small an L2 norm aspossible. A synthetic example shows that the proposed method of extracting FD operatorsand subsequent interpolation works very well. I foresee that the proposed method can beused to reduce the density of receivers (hydrophones or geophones) when designing newstreamers, or with existing equipment to improve the in-line sampling.