Differential Pulse Code Modulation (DPCM)

In a lossy DPCM scheme, m pixels within a causal neighborhood of the current pixel are used to make a linear prediction (estimate) of the pixel's value. More specifically, referring to the raster scan configuration in Fig.7.1, the m pixels prior to the current pixel x_m (shown in the figures as A, B, C, etc.) are used to form a linear prediction denoted by , where

                                  (9.1)

and the 's are the predictor coefficients (weighting factors). To reduce the system complexity, the prediction is usually rounded to the nearest integer, although it may be preserved in floating point representation. It is also necessary to clip the prediction to range [0,2ⁿ-1] for an n-bit image. The differential (error) image, e_m, is constructed as the difference between the prediction and the actual value; i.e.,

                                    (9.2)

Lossless Prediction Coding , the differential image typically has a greatly reduced variance compared to the original image, is significantly less correlated, and has a stable histogram well approximated by a Laplacian (double-sided exponential) distrbution. The difference between lossy and lossless DPCM lies in the handing of the differential image. In order to lower the bit rate, the differential image in lossy DPCM is quantized prior to encoding and transmission. A block diagram for a basic DPCM transmitter and receiver system shown in

Fig. 9.1 , where represents the quantized differential image.

It is important to realize that in forming a prediction, the receiver only has access to the reconstructed pixel values. Since the quantization of the differential image introduces error, the reconstructed values typically differ from the original values. To assure that identical predictions are formed at both the receiver and the transmitter, the transmitter also bases its prediction on the reconstructed values. This is accomplished by containing the quantizer within the prediction loop as shown in the transmitter diagram of Fig.9.1. In essence, each DPCM transmitter includes the receiver within its structure.

The design of a DPCM system consists of optimizing the predictor and the quantizer components. Because the inclusion of the quantizer in the prediction loop results in a complex dependency between the prediction error and the quantization error, a joint optimization should ideally be performed. However, to avoid the complexity of modeling such interactions, the two components are usually optimized separatedly. It has been shown that under the mean-squared error optimization criterion, independent optimizations of the predictor and the quantizer are good approximations to the jointly optimal solution.

Reference:

Digit Image Compression Techniques

Majid Rabbani and Paul W.Jones