Technology scaling enables the design of low cost biosignal processing chips suited for emerging wireless body-area sensing applications. Energy consumption severely limits such applications and memories are becoming the energy bottleneck to achieve ultra-low-power operation. When aggressive voltage scaling is used, memory operation becomes unreliable due to the lack of sufficient Static Noise Margin. This paper introduces an approximate biosignal Compressed Sensing approach. We propose a digital architecture featuring a hybrid memory (6T-SRAM/SCMEM cells) designed to control perturbations on specific data structures. Combined with a statistically robust reconstruction algorithm, the system tolerates memory errors and achieves significant energy savings with low area overhead