Publications by Year: 2008

G. Barrenetxea, F. Ingelrest, Y. M. Lu, and M. Vetterli, “Assessing the challenges of environmental signal processing through the SensorScope project,” in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, USA, 2008, pp. 5149–5152.Abstract

SensorScope is a collaborative project between network, signal processing, and environmental researchers that aims at providing a cheap and out-of-the-box environmental monitoring system based on a wireless sensor network. It has been successfully used in a number of deployments to gather hundreds of megabytes of environmental data. With data gathering techniques well mastered, the efficient processing of the huge amounts of the acquired information to allow for useful exploitation has become an increasingly important issue. In this paper, we present a number of challenging and relevant signal processing tasks that arise from the SensorScope project. We believe the resolution of these problems will benefit from a better understanding of the underlying physical processes. We show an example to demonstrate how physical correlations between different sensing modalities can help reduce the sampling rate.

Y. M. Lu and M. N. Do, “A Mapping-Based Design for Nonsubsampled Hourglass Filter Banks in Arbitrary Dimensions,” IEEE Transactions on Signal Processing, vol. 56, no. 4, pp. 1466-1478, 2008.Abstract

Multidimensional hourglass filter banks decompose the frequency spectrum of input signals into hourglass-shaped directional subbands, each aligned with one of the frequency axes. The directionality of the spectral partitioning makes these filter banks useful in separating the directional information in multi-dimensional signals. Despite the existence of various design techniques proposed for the 2-D case, to our best knowledge, the design of hourglass filter banks in 3-D and higher dimensions with finite impulse response (FIR) filters and perfect reconstruction has not been previously reported. In this paper, we propose a novel mapping-based design for the hourglass filter banks in arbitrary dimensions, featuring perfect reconstruction, FIR filters, efficient implementation using lifting/ladder structures, and a near-tight frame construction. The effectiveness of the proposed mapping-based design depends on the study of a set of conditions on the frequency supports of the mapping kernels. These conditions ensure that we can still get good frequency responses when the component filters used are nonideal. Among all feasible choices, we then propose an optimal specification for the mapping kernels, which leads to the simplest passband shapes and involves the fewest number of frequency variables. Finally, we illustrate the proposed techniques by a design example in 3-D, and an application in video denoising.

Y. M. Lu and M. N. Do, “A Theory for Sampling Signals from a Union of Subspaces,” IEEE Transactions on Signal Processing, vol. 56, no. 6, pp. 2334–2345, 2008.Abstract

One of the fundamental assumptions in traditional sampling theorems is that the signals to be sampled come from a single vector space (e.g., bandlimited functions). However, in many cases of practical interest the sampled signals actually live in a union of subspaces. Examples include piecewise polynomials, sparse representations, nonuniform splines, signals with unknown spectral support, overlapping echoes with unknown delay and amplitude, and so on. For these signals, traditional sampling schemes based on the single subspace assumption can be either inapplicable or highly inefficient. In this paper, we study a general sampling framework where sampled signals come from a known union of subspaces and the sampling operator is linear. Geometrically, the sampling operator can be viewed as projecting sampled signals into a lower dimensional space, while still preserving all the information. We derive necessary and sufficient conditions for invertible and stable sampling operators in this framework and show that these conditions are applicable in many cases. Furthermore, we find the minimum sampling requirements for several classes of signals, which indicates the power of the framework. The results in this paper can serve as a guideline for designing new algorithms for various applications in signal processing and inverse problems.

Y. M. Lu and M. N. Do, “Sampling Signals from a Union of Subspaces,” IEEE Signal Process. Mag., Special Issue on Compressive Sampling, vol. 25, 2008. sampling_union_spaces.pdf