On the Sparsest Representation of Electrocardiograms

In recent years, telecardiology has been growing in significance, due to the shortage of local caregivers in various parts of the world. As the cardiac data volume grows, compact representation becomes imperative in view of bandwidth, storage, power and other constraints. In this backdrop, we present empirical studies on electrocardiogram (ECG) signal representation using a wide variety of wavelet bases. Specifically, we arrange the transform coefficients in decreasing order of magnitude, and count the number of coefficients accounting for 99% of the signal energy (a sparser representation requires less number). We observe that 'Symlet' and 'Daubechies' families generally offer more compact representation compared to Meyer wavelet as well as biorthogonal and reverse biorthogonal families. In particular, the sparsest representation is provided by the 'sym4' (closely followed by the 'db4') wavelet basis for a broad class of ECG signals. Interestingly, this behavior is observed quite consistently across all fifteen (twelve standard and three Frank) leads. Our study assumes significance in the context of basis selection for various ECG signal processing applications, including compression, denoising and compressive sensin

On the Sparsest Representation of Electrocardiograms

In recent years, telecardiology has been growing in significance, due to the shortage of local caregivers in various parts of the world. As the cardiac data volume grows, compact representation becomes imperative in view of bandwidth, storage, power and other constraints. In this backdrop, we present empirical studies on electrocardiogram (ECG) signal representation using a wide variety of wavelet bases. Specifically, we arrange the transform coefficients in decreasing order of magnitude, and count the number of coefficients accounting for 99% of the signal energy (a sparser representation requires less number). We observe that 'Symlet' and 'Daubechies' families generally offer more compact representation compared to Meyer wavelet as well as biorthogonal and reverse biorthogonal families. In particular, the sparsest representation is provided by the 'sym4' (closely followed by the 'db4') wavelet basis for a broad class of ECG signals. Interestingly, this behavior is observed quite consistently across all fifteen (twelve standard and three Frank) leads. Our study assumes significance in the context of basis selection for various ECG signal processing applications, including compression, denoising and compressive sensin

Optimally-balanced Hash Tree Generation in Ad Hoc Networks

Ideally a hash tree is a perfect binary tree with leaves equal to power of two. Each leaf node in this type of tree can represent a mobile node in an ad hoc network. Each leaf in the tree contains hash value of mobile node’s identification (ID) and public key (PK). Such a tree can be used for authenticating PK in ad hoc networks. Most of the previous works based on hash tree assumed perfect hash tree structures, which can be used efficiently only in networks with a specific number of mobile nodes. Practically the number of mobile nodes may not be always equal to a power of two and the conventional algorithms may result in an inefficient tree structure. In this paper the issue of generating a hash tree is addressed by proposing an algorithm to generate an optimally-balanced structure for a complete hash tree. It is demonstrated through both the mathematical analysis and simulation that such a tree is optimally-balanced and can efficiently be used for public key authentication in ad hoc networks

Optimally-balanced Hash Tree Generation in Ad Hoc Networks

Ideally a hash tree is a perfect binary tree with leaves equal to power of two. Each leaf node in this type of tree can represent a mobile node in an ad hoc network. Each leaf in the tree contains hash value of mobile node’s identification (ID) and public key (PK). Such a tree can be used for authenticating PK in ad hoc networks. Most of the previous works based on hash tree assumed perfect hash tree structures, which can be used efficiently only in networks with a specific number of mobile nodes. Practically the number of mobile nodes may not be always equal to a power of two and the conventional algorithms may result in an inefficient tree structure. In this paper the issue of generating a hash tree is addressed by proposing an algorithm to generate an optimally-balanced structure for a complete hash tree. It is demonstrated through both the mathematical analysis and simulation that such a tree is optimally-balanced and can efficiently be used for public key authentication in ad hoc networks