My Ph.D thesis is entitled Linear Pre/Post Filters in Image and Video Coding Systems , and my thesis advisor is Professor John Woods.

My research is on the design of linear pre/post filters for image and video coding systems. The pre/post filters reduce the mean-square-error (MSE) in coding systems by reducing the out-of-band error energy.

The rate-distortion theory for Gaussian sources with memory is best explained using power spectral densities (psd) of the input signal, the coding error signal etc. Without getting into the details, the psd of the overall coding error can be broken into two terms : an in-band or additive noise component and an out-of-band or signal-loss component. In DCT coding for example, those frequency coefficients which are quantized to zero make up the signal-loss component, because the error is equal to the input coefficient/signal itself. In the remaining frequency coefficients, a coarse approximation is transmitted, and the error in this approximation can be described in terms of an external additive noise source.

One very interesting property of the rate-distortion optimal coder is that the in-band and out-of-band components of the overall coding error do not overlap (in the frequency domain). This is in contrast to what happens in practical coders. To analyze what happens in practical coders, we developed analytical expressions for the psd of the coding error in transform/subband/wavelet coding systems, using the so-called gain-plus-additive noise model for quantizers. From such expressions, we can demonstrate that the additive noise (in-band) component of the coding error overlaps with the signal-loss (out-of-band) component. From the expressions, it is also easy to see that one can use pre/post filters to reduce the out-of-band noise energy, thereby improving the coding performance.

The frequency responses of the pre/post filters can be incorporated into the expression for the overall error psd, and this expression can by minimized by imposing reasonable constraints on the filters (FIR, unit DC gain, linear phase etc.). For one-dimensional Gaussian processors, we can show that linear pre/post filters can help DCT-based coders close the gap in performance with respect to subband/wavelet coders. When coding natural images, we can reduce the overall MSE by using spatially adaptive pre/post filters. For example, by using two sets of separable 5x5 postfilters, the PSNR of the JPEG-coded Lena image increases by about 1 dB at a rate of 0.25 bits/pixel.

We also apply the gain-plus-additive noise model to obtain a linear system representation of a DPCM scheme. This leads to a frequency domain description of the DPCM system, and to a demonstration that at low rates, the DPCM coding error contains a significant amount of out-of-band noise energy. We subsequently develop the theory of designing linear pre/post filters for DPCM coders.

The theory developed so far, for DCT-based coders and for DPCM coders is combined to design spatio-temporal linear pre/post filters for video coders. Simulation results are presented in the full thesis. For MPEG-2 coding of the SIF version of Flower Garden at 2.3 Mbps, with a GOP of 15 frames, we find that using two classes of 3-tap temporal and 5x5-tap spatial postfilters provides PSNR gains of roughly 1 dB for I frames, and roughly 0.6 dB for P and B frames.

Publications related to the above work can be downloaded from http://cipr.rpi.edu/anil/ICIP97/publications.html