Transform-Based Distributed Data Gathering

Abstract

A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These transforms can be computed as data is routed towards the collection (or sink) node in the tree and exploit data correlation between nodes in the tree. Moreover, when used in wireless sensor networks, these transforms can also leverage data received at nodes via broadcast wireless communications. Various constructions of unidirectional transforms are also provided for use in data gathering in wireless sensor networks. New wavelet transforms are also proposed which provide significant improvements over existing unidirectional transforms.

Directional Transforms for Video Coding Based on Lifting on Graphs

“…u k,j ) filte . Note that inverting the operations of the forward transform to obtain the inverse transform is straightforward from (3) as long as only connections between U and P nodes are used for filtering Lifting transforms on graphs can operate with arbitrary graphs, P j /U j disjoint splittings and p j and u j filte designs without compromising the perfect reconstruction and critically sampled properties of the transform [36]. This fl xibility in the design makes the choice of the transform parameters a crucial task in order to achieve an efficien transformation.…”

Compression in wireless sensor networks

“…These improvements are mostly due to unidirectional computation of the 2D transform and the e↵ectiveness of unidirectional computation in o↵setting excessively high local communication costs, especially in the backward direction. The main objective of a recent work [Shen 2010] is to find a general set of en-route in-network (or unidirectional) transforms for given routing trees and schedules in conjunction with a set of conditions for their invertibility. This general set includes a wide range of existing unidirectional transforms and has also inspired new transform designs which perform better than existing transforms in the context of data gathering in WSNs.…”

“…Optimal operation requires cross-layer or multi-layer coordination between application layer compression and MAC layer scheduling. The dependency of compression on routing is obvious [Shen 2010;Scaglione and Servetto 2002]. Furthermore, incorporation of resource awareness in compression schemes, for example dependency on remaining energy, requires coordination between application layer compression and the physical layer.…”

Signal compression in wireless sensor networks

“…In the case where these constraints are severe and rigid, the compression algorithm design must carefully balance these additional constraints with the resulting compression rate and distortion achieved. [5] T O S D N C distributed source coding [2] SO SD DSC distributed KLT [6] SO, ST SD DTC tree KLT [7] SO RC DTC tree-based wavelets [8] SO SD, CR DTC graph-based wavelets [9] SO RC DTC distributed compressive sensing [10] S T S D C S compressive wireless sensing [11] S O C R C S randomized gossiping [12] SO, TO, ST CR CS sparse random projections [13] SO, TO, ST CR CS localized compressive sensing [14] S T J O C S T-DPCM [15] SO JO DPC…”

“…(ii) Graph-based wavelets While the irregular wavelet transform makes use of node proximity regardless of network topology (compression over routing), graph-based wavelets [9,[23][24][25] use a lifting transform constructed on the network communications graph (routing over compression). The partitioning step chooses odd nodes that provide maximal decorrelation.…”