We propose a sparsity-based simplification method for Spectral Domain Optical Coherence Tomography (SD-OCT) images of cardiac samples, displaying layers of tissue. Inspired by the Compressed Sensing (CS) theory, we implement a dedicated sparse sampling of SD-OCT samples achieving image simplification suited for layers segmentation, which is the target application. We validate a straightforward segmentation approach on the variance map of the simplified images against manual delineation on raw SD-OCT images of in-vitro biological samples from four human hearts. We also correlate average layer thickness with histopathological measures. Finally, we compare our simplified images to state of the art denoising approaches.