Online energy reconstruction for calorimeters under high pile-up conditions using deconvolutional techniques

High-energy calorimeters operating at high data acquisition rate may suffer from signal superposition (pile-up) in their electronic readout. This problem occurs whenever the time interval among two subsequent incoming physics signatures is shorter than the front-end electronics time latency. Signal pile-up may cause severe problems on the online energy estimation and some palliative solutions, treating the pile-up signals as an additional noise source, have been proposed in order to preserve the well established Optimal Filter theory as the signal estimation baseline design. In order to produce actual online compensation for pile-up effect, the method proposed in this paper approximates the front-end electronics as a linear transmission channel whose transfer function can be linearly equalized (unconvolved). For experiments where the acquisition rate is synchronized with the collision clock, the equalizer output provides a straightforward energy estimation per bunch-crossing (BC). Optimal approximations for the equalizer design are proposed using both FIR (Finite Impulse Response) filters and an iterative method. The latter offers better reconstruction performance (smaller errors), but has higher computational cost and requires extra data-flow circuitry when online implementation is envisaged. Toy simulation data that consider typical calorimeter front-end responses are used to evaluate the performance of the proposed methods.