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A growing interest has recently been observed in energy sensitive pixel array for high flux X-ray imaging. These devices provide compositional analysis of the imaged objects and would be useful in a wide range of applications in the field of security, non destructive testing and medical imaging. CEA-LETI has developed a CdTe linear array pixel detector coupled with a novel 16-channels fast readout circuit. For each channel, the signal is continuously digitized by a 100 MHz 12 bit ADC and a FPGA controls acquisition and reconstructs the energy spectra on 256 bins. The readout circuit is coupled with a 3 mm thick CdTe 16 pixels linear array detector 0.8 mm pixel pitch. Thanks to this innovative architecture of the read-out circuit it is possible to perform advanced signal processing in real time including pile-up rejection and charge sharing correction. In this work, we study the possibility of correcting the effect of charge sharing. Although the pixel size is relatively large, charge sharing events contribute to 40 to 60% of all events and significantly degrade the spectrometric response of the detector. By summing the amplitude pulses from two neighboring pixels, we can recover the accurate information from the photon energy. This correction technique has been successfully tested with a monochromatic X-ray micro beam at ESRF.