The Experts below are selected from a list of 987 Experts worldwide ranked by ideXlab platform
Richard G. Baraniuk - One of the best experts on this subject based on the ideXlab platform.
-
Representation and compression of multidimensional piecewise functions using surflets
2009Co-Authors: Student Member, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:Abstract—We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M 0 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate–distortion performance; for piecewise smooth functions, our Coder has near-optimal rate–distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, whic
-
Representation and Compression of Multidimensional Piecewise Functions Using Surflets
IEEE Transactions on Information Theory, 2009Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results on synthetic signals provide a comparison between surflet-based Coders and previously studied approximation schemes based on wedgelets and wavelets.
-
Sparse sign...
2008Co-Authors: Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
-
Representation and compression of multi-dimensional piecewise functions using surflets
2006Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
Venkat Chandrasekaran - One of the best experts on this subject based on the ideXlab platform.
-
Representation and Compression of Multidimensional Piecewise Functions Using Surflets
IEEE Transactions on Information Theory, 2009Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results on synthetic signals provide a comparison between surflet-based Coders and previously studied approximation schemes based on wedgelets and wavelets.
-
Representation and compression of multi-dimensional piecewise functions using surflets
2006Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
Michael B. Wakin - One of the best experts on this subject based on the ideXlab platform.
-
Representation and compression of multidimensional piecewise functions using surflets
2009Co-Authors: Student Member, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:Abstract—We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M 0 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate–distortion performance; for piecewise smooth functions, our Coder has near-optimal rate–distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, whic
-
Representation and Compression of Multidimensional Piecewise Functions Using Surflets
IEEE Transactions on Information Theory, 2009Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results on synthetic signals provide a comparison between surflet-based Coders and previously studied approximation schemes based on wedgelets and wavelets.
-
Sparse sign...
2008Co-Authors: Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
-
Representation and compression of multi-dimensional piecewise functions using surflets
2006Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
Dror Baron - One of the best experts on this subject based on the ideXlab platform.
-
Representation and compression of multidimensional piecewise functions using surflets
2009Co-Authors: Student Member, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:Abstract—We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M 0 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate–distortion performance; for piecewise smooth functions, our Coder has near-optimal rate–distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, whic
-
Representation and Compression of Multidimensional Piecewise Functions Using Surflets
IEEE Transactions on Information Theory, 2009Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results on synthetic signals provide a comparison between surflet-based Coders and previously studied approximation schemes based on wedgelets and wavelets.
-
Sparse sign...
2008Co-Authors: Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
-
Representation and compression of multi-dimensional piecewise functions using surflets
2006Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
Baraniuk, Richard G. - One of the best experts on this subject based on the ideXlab platform.
-
Representation and compression of multidimensional piecewise functions using surflets
'Institute of Electrical and Electronics Engineers (IEEE)', 2008Co-Authors: Chandrasekaran Venkat, Baron Dror, Wakin, Michael B., Baraniuk, Richard G.Abstract:We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results on synthetic signals provide a comparison between surflet-based Coders and previously studied approximation schemes based on wedgelets and wavelets.Texas Instruments Leadership University ProgramUnited States. Air Force Research Laboratory (Grant FA8650-051850)Air Force Office of Scientific Research (United States) (Grant FA9550-04-0148)United States. Office of Naval Research (Grant N00014-02-1-0353)National Science Foundation (Grant CCF-0431150
-
Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets
2006Co-Authors: Chandrasekaran Venkat, Wakin Michael, Baron Dror, Baraniuk, Richard G.Abstract:Journal PaperWe study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution Predictive Coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our Coder has near-optimal rate-distortion performance. Our Coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our Coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results demonstrate that surflets provide superior compression performance when compared to other state-of-the-art approximation schemes
