Image-scrambling schemes are designed to render the image content unintelligible. Wyner has proposed an elegant one-dimensional (1-D) scrambling scheme without bandwidth expansion, making use of the discrete prolate spheroidal sequences (DPSS). The DPSS are optimal regarding their energy concentration in a given frequency subband. In this paper, we propose the two-dimensional (2-D) extension and application of this algorithm. We discuss new possibilities introduced by the 2-D approach. We also include experimental results.