Reconstruction of temporal-spatial profile from participatory sensing data using Compressive Sensing ∗ Rajib Kumar Rana , Chun Tung Chou , Salil Kanhere School of Computer Science and Engineering, University of New South Wales, Sydney, Australia rajibr@cse.unsw.edu.au , ctchou@cse.unsw.edu.au , salilk@cse.unsw.edu.au Abstract The reconstruction of an unknown temporal-spatial pro- file from participatory sensing data poses a number of chal- lenges due to uncoordinated user movement and possibly low user involvement. This paper considers the problem of reconstructing such a profile from participatory sensing data by exploiting the theory of compressive sensing. In partic- ular we study the impact of the number of users and oppor- tunistic user communication on the reconstruction accuracy. Our simulation results show that, in the case where each user is limited to return one projection, a small amount of local data exchange between the users can improve the reconstruc- tion accuracy. 1 Introduction Participatory sensing [1] aims to address the challenges in large-scale data collection by involving community in the data collection process. It leverages the human held mo- bile phones as sensors because of their ubiquity and embed- ded capabilities such as the capturing of acoustics signals and data processing. A proposed application of participatory sensing is to measure urban noise pollution level by mobile phones as their owners go on with their own business. In such an application, an important issue is the accuracy of the temporal-spatial profile achieved by the measurements col- lected from participatory sensing. However, the typical setting of participatory sensing makes the accurate reconstruction of such temporal-spatial profiles challenging. Firstly, the uncoordinated and random movement of the participants means that important features of the profile may not be captured. Secondly, the number of contributing participants may be low. Thirdly, the limited and expensive cellular bandwidth may discourage contribu- ∗ This research is sponsored by the Australian Research Council Discovery Grant DP0770523. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SenSys’07 November 6–9, 2007, Sydney, Australia. Copyright 2007 ACM ...$5.00 tions. All the above challenges essentially initiate several in- teresting research questions, such as: What will be the qual- ity of re-construction that can be obtained from an unpre- dictable number of randomly moving mobile phone users? Can we use the theory of compressive sensing to achieve a good-quality reconstruction from these participatory sensing data? Since local communications between users, e.g. by WiFi or Bluetooth, is cheap and has plentiful bandwidth, can we exploit opportunistic communication between users to re- duce the amount of cellular bandwidth required but without degrading reconstruction accuracy? In this paper, we will present some preliminary work on using the theory of compressive sensing [2] in reconstruct- ing the temporal-spatial profile from the participatory sens- ing data to address the above research questions. Our work also exploits opportunistic user communication to reduce the amount of the cellular bandwidth required. In the next sec- tion we give an overview of compressive sensing and a dis- cussion on its application to participatory sensing. 2 Compressive sensing and its application to participatory sensing The theory of compressive sensing has greatly refined the traditional sampling theory by Nyquist which states that a band-limited signal with bandwidth f must be sampled at least 2 f times per second for it to be re-constructed perfectly. However, real signals are not band-limited and it would be rare for samples from participatory sensing to be measured at regular intervals. Fortunately, compressive sensing elim- inated the band-limited and regular sampling requirements. Instead, the theory of compressive sensing says that the num- ber of measurements required to re-construct an unknown signal depends on how sparse the unknown signal is. Also, instead of performing point-wise measurement, compressive sensing requires that a number of projections be measured. We will illustrate the concept of compressive sensing by showing how an unknown vector x ∈ R N can be re- constructed. (Note: Any multi-dimensional temporal-spatial profile can easily be turned into a vector.) Let Φ ∈ R M×N be a projection matrix, then the projection of the unknown vector x onto the rows of the projection matrix Φ is: y = Φx (1) The theory of compressive sensing provides a method to re- construct the unknown vector x from the projections (or mea-