Multiscale Information Processing and Commuications

Many critical scientific and engineering applications rely upon the accurate reconstruction of spatially or temporally distributed phenomena from measured data. However, a number of information processing challenges arise routinely in these problems. Sensing is often indirect in nature, such as tomographic projections in medical imaging, resulting in complicated inverse reconstruction problems. The sensing can also be decentralized, as in wireless sensor networks, leading to complex tradeoffs between communications, sensing and processing. Furthermore, in any practical system, the measurements are noisy due to errors in sensing and/or quantization effects. In addition to the issues associated with sensing, the behavior of the information-bearing signals of interest may be very rich and complex, and consequently difficult to model a priori. All of these issues combine to make accurate reconstruction a complicated task, involving a myriad of system-level and algorithm tradeoffs.

In this talk, I will demonstrate that nonparametric multiscale reconstruction methods can overcome all the challenges above and provide a theoretical framework for assessing tradeoffs between reconstruction accuracy and system resources. First, the theory supporting these methods facilitates characterization of fundamental performance limits. Examples include lower bounds on the best achievable error performance in medical image reconstruction and upper bounds on the total amount of power that must be consumed to perform a sensor network task. Second, the methods themselves are practical and resource-efficient in a broad range of contexts, including a diverse variety of sensing modalities, noise models, data dimensionalities, and error metrics. Third, existing reconstruction methods can often be enhanced with multiscale techniques…