A novel approach to design a robust and optimal scalar quantizer for any non-standard input density

This paper proposes a method for the design of adaptive scalar quantizer based on the source statistics. Adaptivity is useful in applications where the statistics of the source are either not known a priori or will change over time. The proposed method first determines two quantizer cells and the corresponding output levels such that the distortion is minimized over all possible two-level quantizers. Then the cell with the largest empirical distortion is split into two cells in such a way that the empirical distortion is minimized over all possible splits. Each time a split is made, the number of output levels increases by one until the target number of cells is reached. Finally, the resultant quantizer serves as a good initial starting point for running the Lloyd-Max Algorithm in order to reach global optimality. Experimental results show that this new designed quantizer outperforms that obtained by the Lloyd-Max method started with an arbitrary initial point in terms of Mean Square Error (MSE). Moreover, the proposed method converges more rapidly than the Lloyd-Max one. Our method adapts itself to the histogram of the data without creating any empty output range. This feature improves the robustness of the design method.