This paper presents a transform coding technique for non-rectangular 2-D signals by extending the signal into a rectangular block in order to enable conventional block-based transform coding. The technique could be suitable for coding residuals of prediction blocks using geometric partitioning which has been adopted into the draft Versatile Video Coding standard. The extension of the non-rectangular signal is found using a sparse solution set generated by applying Orthogonal Matching Pursuits using partitioned transform bases. The method developed in this paper is based on Discrete Cosine Transform. Results achieved in an experimental setup outside of the video coding loop are presented for signals of triangular and trapezoidal shape in comparison to the shape-adaptive DCT. Encouraging gains are observed specifically for larger block sizes and in dependency of the quantization parameter and the partitioning shape.