Magnetic resonance spectroscopic imaging (MRSI) has multiple interests in clinical practice but it faces quite long acquisition time in practice which limits their use in a clinical environment. In this work, a new fast Magnetic Resonance Spectroscopic image acquisition method, based on Compressed Sensing and the a priori known support of the metabolites chemical shift, is introduced and evaluated based on a k-t space spiral sampling. In the real-world noisy scenario the error in the recovered spectrum highly depends on the acquired samples. We reduce this error to an acceptable level by selecting irregularly the samples using the Sequential Backward Selection algorithm. Our method has been applied on an in vivo 31P acquisition, to prove the feasibility of the proposed approach.