Directional block transforms (DBTs), such as discrete Fourier transforms, are basically less efficient for sparse image representation
than directional overlapped transforms, such as curvelet and contourlet, but have advantages in practical computation, such as less computational cost, less amount of memory usage to be used, and parallel processing. In order to realize efficient DBTs, this paper proposes
directional discrete cosine transforms (DDCTs) by using discrete cosine and sine transforms. The resulting transforms provide richer directional orientations of atoms than conventional DBTs, and thus they are expected to be more efficient for image analysis and processing. In experiments, we evaluate DDCTs with conventional DBTs in image recovery by a convex optimization.