Quantification of T2 values is valuable for a wide range of research and clinical applications. Multi-echo spin echo protocols allow mapping T2 values, yet, at the cost of strong contamination from stimulated echoes. The echo-modulation-curve algorithm can efficiently overcome these limitations to produce accurate T2 values. Still, integration into clinical routine requires further acceleration in scan time. In this work we present a fixed-rank and sparse algorithm (SPARK) for accelerating the acquisition of T2 values, and compare it against standard L+S and GRAPPA. SPARK was found to improve robustness to reconstruction parameters, and achieve superior accuracy at high acceleration factors.