  Given a set of samples, a few of them being possibly saturated, we propose an
efficient algorithm in order to cancel saturation while reconstructing
band-limited signals. Our method satisfies a minimum-loss constraint and relies
on sinc-related bases. It involves matrix inversion and is a direct,
non-iterative approach. It consists of two main steps: (i) regression, to
estimate the expansion coefficients of the signal model; (ii) interpolation, to
restore an estimated value for those samples that are saturated. Because the
proposed method is free from tuning parameters, it is hardware-friendly and we
expect that it will be particularly useful in the context of orthogonal
frequency-division multiplexing. There, the high peak-to-average power ratio of
the transmitted signal results in a challenging decoding stage in the presence
of saturation, which causes significant decoding errors due to the nonlinearity
of amplifiers and receivers, ultimately resulting in band distortion and
information loss. Our experiments on realistic simulations confirm that our
proposed reconstruction of the saturated samples can significantly reduce
transmission errors in modern high-throughput digital-communication receivers.
