Prosthetic limbs would benefit from tactile feedback to provide sensory information when interacting with the environment, such as adjusting grasps using force feedback or palpating texture. In this work, we demonstrate how a multilayer tactile sensor can be used for palpation, and enhance the ability to discriminate between touch interfaces. Inspired by mechanoreceptors in skin, the multilayer sensor consists of multiple textile force sensing elements. The novelty of this work lies in the application of a multilayer sensor, one that produces touch receptor like (neuromorphic) output, to texture classification by using a classifier based on sparse recovery. This approach is shown to be capable of palpation, achieving classification accuracies as high as 97% on a distinct texture set. Using compressed sensing and sparse recovery, the multilayer sensor can decode texture under dynamic conditions, potentially providing amputees the ability to perceive rich haptic information while using their prosthesis.