Separable cosparse Analysis Operator learning. Seibert, M., Wörmann, J., Gribonval, R., & Kleinsteuber, M. In *2014 22nd European Signal Processing Conference (EUSIPCO)*, pages 770-774, Sep., 2014.

Paper abstract bibtex

Paper abstract bibtex

The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose an algorithm for learning a cosparse Analysis Operator that adheres to the preexisting structure of the data, and thus allows for a very efficient implementation. This is achieved by enforcing a separable structure on the learned operator. Our learning algorithm is able to deal with multidimensional data of arbitrary order. We evaluate our method on volumetric data at the example of three-dimensional MRI scans.

@InProceedings{6952253, author = {M. Seibert and J. Wörmann and R. Gribonval and M. Kleinsteuber}, booktitle = {2014 22nd European Signal Processing Conference (EUSIPCO)}, title = {Separable cosparse Analysis Operator learning}, year = {2014}, pages = {770-774}, abstract = {The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose an algorithm for learning a cosparse Analysis Operator that adheres to the preexisting structure of the data, and thus allows for a very efficient implementation. This is achieved by enforcing a separable structure on the learned operator. Our learning algorithm is able to deal with multidimensional data of arbitrary order. We evaluate our method on volumetric data at the example of three-dimensional MRI scans.}, keywords = {biomedical MRI;data analysis;fast Fourier transforms;inverse transforms;learning (artificial intelligence);medical image processing;separable cosparse analysis operator learning;sparse representation;data analysis;vectorized signals;three-dimensional MRI scans;MAOL;multilinear algebra;geometric optimization;Tensile stress;Magnetic resonance imaging;Algorithm design and analysis;Image reconstruction;Analytical models;Noise;Signal processing algorithms;Cosparse Analysis Model;Analysis Operator Learning;Sparse Coding;Separable Filters}, issn = {2076-1465}, month = {Sep.}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924571.pdf}, }

Downloads: 0

{"_id":"pCpxHM4uXq7CfiRg3","bibbaseid":"seibert-wrmann-gribonval-kleinsteuber-separablecosparseanalysisoperatorlearning-2014","authorIDs":[],"author_short":["Seibert, M.","Wörmann, J.","Gribonval, R.","Kleinsteuber, M."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","author":[{"firstnames":["M."],"propositions":[],"lastnames":["Seibert"],"suffixes":[]},{"firstnames":["J."],"propositions":[],"lastnames":["Wörmann"],"suffixes":[]},{"firstnames":["R."],"propositions":[],"lastnames":["Gribonval"],"suffixes":[]},{"firstnames":["M."],"propositions":[],"lastnames":["Kleinsteuber"],"suffixes":[]}],"booktitle":"2014 22nd European Signal Processing Conference (EUSIPCO)","title":"Separable cosparse Analysis Operator learning","year":"2014","pages":"770-774","abstract":"The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose an algorithm for learning a cosparse Analysis Operator that adheres to the preexisting structure of the data, and thus allows for a very efficient implementation. This is achieved by enforcing a separable structure on the learned operator. Our learning algorithm is able to deal with multidimensional data of arbitrary order. We evaluate our method on volumetric data at the example of three-dimensional MRI scans.","keywords":"biomedical MRI;data analysis;fast Fourier transforms;inverse transforms;learning (artificial intelligence);medical image processing;separable cosparse analysis operator learning;sparse representation;data analysis;vectorized signals;three-dimensional MRI scans;MAOL;multilinear algebra;geometric optimization;Tensile stress;Magnetic resonance imaging;Algorithm design and analysis;Image reconstruction;Analytical models;Noise;Signal processing algorithms;Cosparse Analysis Model;Analysis Operator Learning;Sparse Coding;Separable Filters","issn":"2076-1465","month":"Sep.","url":"https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924571.pdf","bibtex":"@InProceedings{6952253,\n author = {M. Seibert and J. Wörmann and R. Gribonval and M. Kleinsteuber},\n booktitle = {2014 22nd European Signal Processing Conference (EUSIPCO)},\n title = {Separable cosparse Analysis Operator learning},\n year = {2014},\n pages = {770-774},\n abstract = {The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose an algorithm for learning a cosparse Analysis Operator that adheres to the preexisting structure of the data, and thus allows for a very efficient implementation. This is achieved by enforcing a separable structure on the learned operator. Our learning algorithm is able to deal with multidimensional data of arbitrary order. We evaluate our method on volumetric data at the example of three-dimensional MRI scans.},\n keywords = {biomedical MRI;data analysis;fast Fourier transforms;inverse transforms;learning (artificial intelligence);medical image processing;separable cosparse analysis operator learning;sparse representation;data analysis;vectorized signals;three-dimensional MRI scans;MAOL;multilinear algebra;geometric optimization;Tensile stress;Magnetic resonance imaging;Algorithm design and analysis;Image reconstruction;Analytical models;Noise;Signal processing algorithms;Cosparse Analysis Model;Analysis Operator Learning;Sparse Coding;Separable Filters},\n issn = {2076-1465},\n month = {Sep.},\n url = {https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924571.pdf},\n}\n\n","author_short":["Seibert, M.","Wörmann, J.","Gribonval, R.","Kleinsteuber, M."],"key":"6952253","id":"6952253","bibbaseid":"seibert-wrmann-gribonval-kleinsteuber-separablecosparseanalysisoperatorlearning-2014","role":"author","urls":{"Paper":"https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924571.pdf"},"keyword":["biomedical MRI;data analysis;fast Fourier transforms;inverse transforms;learning (artificial intelligence);medical image processing;separable cosparse analysis operator learning;sparse representation;data analysis;vectorized signals;three-dimensional MRI scans;MAOL;multilinear algebra;geometric optimization;Tensile stress;Magnetic resonance imaging;Algorithm design and analysis;Image reconstruction;Analytical models;Noise;Signal processing algorithms;Cosparse Analysis Model;Analysis Operator Learning;Sparse Coding;Separable Filters"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"inproceedings","biburl":"https://raw.githubusercontent.com/Roznn/EUSIPCO/main/eusipco2014url.bib","creationDate":"2021-02-13T17:43:41.633Z","downloads":0,"keywords":["biomedical mri;data analysis;fast fourier transforms;inverse transforms;learning (artificial intelligence);medical image processing;separable cosparse analysis operator learning;sparse representation;data analysis;vectorized signals;three-dimensional mri scans;maol;multilinear algebra;geometric optimization;tensile stress;magnetic resonance imaging;algorithm design and analysis;image reconstruction;analytical models;noise;signal processing algorithms;cosparse analysis model;analysis operator learning;sparse coding;separable filters"],"search_terms":["separable","cosparse","analysis","operator","learning","seibert","wörmann","gribonval","kleinsteuber"],"title":"Separable cosparse Analysis Operator learning","year":2014,"dataSources":["A2ezyFL6GG6na7bbs","oZFG3eQZPXnykPgnE"]}