A mode-mixing cavity, consisting of an electrically-large rectangular cavity with one deformed corner, supports distinct modes as a function of driving frequency. Perforating one side of this cavity, the modes formed within can be projected into an imaging domain, multiplexing the scene's spatial content into backscattered signals that is post-processed to obtain high-quality images. While this device has shown great promise as a platform for computational imaging at microwave frequencies, its premise necessitates a large bandwidth, a requirement that complicates circuit design and may not be readily available. In this presentation, we propose and report preliminary experimental results for a cavity containing a tunable artificial impedance surface in one of its walls. By varying the electromagnetic response of the cavity's boundary the field distribution within the cavity can be altered, thus generating distinct radiation patterns without a large bandwidth.