# Signal Processing

Our research in the area of signal processing has been mainly on the following:

Signal processing for space-time wireless communications has been described separately.

## Discrete signal processing

Suppose a source with unknown distribution is observed after going through a discrete memoryless channel with known transition matrix. The denoising problem is to generate an estimate of the underlying noise-free sequence given the noisy observations. Weissman et al, (2004) recently proposed a discrete universal denoising algorithm (DUDE) and asymptotic analysis for this problem. The central idea in this elegant approach is to compute for each position of the noisy sequence, an empirical distribution of its occurences within a context, i.e., a bi-directional window. We made a connection between this and string matching techniques commonly used in computer science. Using this, we are able to design more efficient denoising algorithms, even when the context sizes are larger than the regularity condition needed in DUDE. Also, we looked at loss estimation methods that allow us to choose appropriate context sizes for improving denoising of particular observations. This is a topic of on-going research.

## Geometry signal processing

Many problems in computer graphics requires faithful reconstruction of a given scene which has been constructed through given primitive elements. Information about a scalar distance field (i.e., distance to a point on scene closest to a given point of observation) might be used to reconstruct the scene. We have looked into efficient algorithms to compute such distance fields using the $l_\infty$ distance metric that allows us to reliably localize the surface of interest. This also leads to the question of how to place the sampling points in 3-dimensional space in order to minimize the reconstruction distortion.

## Wireless video coding

Signal processing for multi-terminal source coding has been described separately.

In source transmission schemes over noisy channels considerable performance gains can be obtained if we utilize the characteristics of the payload (such as voice, images, video etc.). The source-channel separation theorem (Cover and Thomas, Elements of Information Theory, 1991) implies that we can separate the problems of source compression and channel transmission. However, for finite complexity and delay we can obtain significant gains through source-channel coding. We proposed a source-channel coding scheme in which a scalable source coding scheme was combined with Rate Compatible Punctured Codes (RCPC) (Hagenauer, 1988). The flexibility offered by this scheme is ideally suited for the uncertain wireless environment and results using images over realistic wireless channels demonstrated this property.