Texas Two-Step: A Framework for Optimal Multi-Input Single-Output Deconvolution
Multi-input single-output deconvolution (MISO-D) aims to extract a deblurred estimate of a target signal from several blurred and noisy observations. This paper develops a new two step framework-Texas two-step-to solve MISO-D problems with known blurs. Texas two-step first reduces the MISO-D problem...
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| Veröffentlicht in: | IEEE transactions on image processing 2007-11, Vol.16 (11), p.2752-2765 |
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| container_title | IEEE transactions on image processing |
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| creator | Neelamani, R.N. Deffenbaugh, M. Baraniuk, R.G. |
| description | Multi-input single-output deconvolution (MISO-D) aims to extract a deblurred estimate of a target signal from several blurred and noisy observations. This paper develops a new two step framework-Texas two-step-to solve MISO-D problems with known blurs. Texas two-step first reduces the MISO-D problem to a related single-input single-output deconvolution (SISO-D) problem by invoking the concept of sufficient statistics (SSs) and then solves the simpler SISO-D problem using an appropriate technique. The two-step framework enables new MISO-D techniques (both optimal and suboptimal) based on the rich suite of existing SISO-D techniques. In fact, the properties of SSs imply that a MISO-D algorithm is mean-squared-error optimal if and only if it can be rearranged to conform to the Texas two-step framework. Using this insight, we construct new wavelet- and curvelet-based MISO-D algorithms with asymptotically optimal performance. Simulated and real data experiments verify that the framework is indeed effective. |
| doi_str_mv | 10.1109/TIP.2007.906251 |
| format | Article |
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This paper develops a new two step framework-Texas two-step-to solve MISO-D problems with known blurs. Texas two-step first reduces the MISO-D problem to a related single-input single-output deconvolution (SISO-D) problem by invoking the concept of sufficient statistics (SSs) and then solves the simpler SISO-D problem using an appropriate technique. The two-step framework enables new MISO-D techniques (both optimal and suboptimal) based on the rich suite of existing SISO-D techniques. In fact, the properties of SSs imply that a MISO-D algorithm is mean-squared-error optimal if and only if it can be rearranged to conform to the Texas two-step framework. Using this insight, we construct new wavelet- and curvelet-based MISO-D algorithms with asymptotically optimal performance. Simulated and real data experiments verify that the framework is indeed effective.</description><identifier>ISSN: 1057-7149</identifier><identifier>EISSN: 1941-0042</identifier><identifier>DOI: 10.1109/TIP.2007.906251</identifier><identifier>PMID: 17990752</identifier><identifier>CODEN: IIPRE4</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algorithms ; Applied sciences ; Artificial Intelligence ; Astronomy ; Asymptotic properties ; Biomedical imaging ; Blurred ; Computer simulation ; Curvelets ; deblurring ; Deconvolution ; Digital filters ; Estimates ; Exact sciences and technology ; Frequency estimation ; Image Enhancement - methods ; Image Interpretation, Computer-Assisted - methods ; Image processing ; Image restoration ; Information, signal and communications theory ; minimax optimal ; Minimax techniques ; Miscellaneous ; multichannel ; Nonlinear filters ; Optimization ; Regression Analysis ; Reproducibility of Results ; restoration ; Sensitivity and Specificity ; Signal processing ; Statistics ; sufficient statistics ; Telecommunications and information theory ; Telescopes ; wavelet-vaguelette ; wavelets</subject><ispartof>IEEE transactions on image processing, 2007-11, Vol.16 (11), p.2752-2765</ispartof><rights>2007 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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This paper develops a new two step framework-Texas two-step-to solve MISO-D problems with known blurs. Texas two-step first reduces the MISO-D problem to a related single-input single-output deconvolution (SISO-D) problem by invoking the concept of sufficient statistics (SSs) and then solves the simpler SISO-D problem using an appropriate technique. The two-step framework enables new MISO-D techniques (both optimal and suboptimal) based on the rich suite of existing SISO-D techniques. In fact, the properties of SSs imply that a MISO-D algorithm is mean-squared-error optimal if and only if it can be rearranged to conform to the Texas two-step framework. Using this insight, we construct new wavelet- and curvelet-based MISO-D algorithms with asymptotically optimal performance. 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This paper develops a new two step framework-Texas two-step-to solve MISO-D problems with known blurs. Texas two-step first reduces the MISO-D problem to a related single-input single-output deconvolution (SISO-D) problem by invoking the concept of sufficient statistics (SSs) and then solves the simpler SISO-D problem using an appropriate technique. The two-step framework enables new MISO-D techniques (both optimal and suboptimal) based on the rich suite of existing SISO-D techniques. In fact, the properties of SSs imply that a MISO-D algorithm is mean-squared-error optimal if and only if it can be rearranged to conform to the Texas two-step framework. Using this insight, we construct new wavelet- and curvelet-based MISO-D algorithms with asymptotically optimal performance. Simulated and real data experiments verify that the framework is indeed effective.</abstract><cop>New York, NY</cop><pub>IEEE</pub><pmid>17990752</pmid><doi>10.1109/TIP.2007.906251</doi><tpages>14</tpages></addata></record> |
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| subjects | Algorithms Applied sciences Artificial Intelligence Astronomy Asymptotic properties Biomedical imaging Blurred Computer simulation Curvelets deblurring Deconvolution Digital filters Estimates Exact sciences and technology Frequency estimation Image Enhancement - methods Image Interpretation, Computer-Assisted - methods Image processing Image restoration Information, signal and communications theory minimax optimal Minimax techniques Miscellaneous multichannel Nonlinear filters Optimization Regression Analysis Reproducibility of Results restoration Sensitivity and Specificity Signal processing Statistics sufficient statistics Telecommunications and information theory Telescopes wavelet-vaguelette wavelets |
| title | Texas Two-Step: A Framework for Optimal Multi-Input Single-Output Deconvolution |
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