Short-T2 imaging needs immediate and rapid encoding, as provided by zero echo time (ZTE) MRI. However, in ZTE, excitation and early encoding occur simultaneously and preclude data acquisition in the k-space center, leading to local undersampling or gap. One way of retrieving the missing data involves algebraic reconstruction, but it is limited to small gaps and thus requires short RF pulses that restrain achievable SNR and contrast options. Here, we demonstrate a method for algebraic reconstruction of large gaps, based on the knowledge of excitation pulses. It enables the use of longer pulses and overcomes ZTE flip angle limitations.