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On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary

Javier S. Turek, Irad Yavneh, Michael Elad
<span title="">2011</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gkn2pu46ozb4tmkxczacnmtvkq" style="color: black;">IEEE Transactions on Signal Processing</a> </i> &nbsp;
Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling.  ...  In this work we analyze two Bayesian denoising algorithms -- the Maximum-Aposteriori Probability (MAP) and the Minimum-Mean-Squared-Error (MMSE) estimators, under the assumption that the dictionary is  ...  A signal w is said to have a sparse representation over a known dictionary, D ∈ R n×m , if there exists a sparse vector x ∈ R m such that w = Dx.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2011.2151190">doi:10.1109/tsp.2011.2151190</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/un62dqcbjfgmjmkugcd7r4cmiy">fatcat:un62dqcbjfgmjmkugcd7r4cmiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401055346/http://www.cs.technion.ac.il/~elad/publications/journals/2009/Unitary_Bounds_ACHA.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/59/b3/59b3125c8ece8d061a0b58b7d079d6f82599e09b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2011.2151190"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Closed-form mmse estimator for denoising signals under sparse representation modelling

Matan Protter, Irad Yavneh, Michael Elad
<span title="">2008</span> <i title="IEEE"> 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel </i> &nbsp;
This paper deals with the signal denoising problem, assuming a prior based on a sparse representation with respect to a unitary dictionary.  ...  We demonstrate this formula, and compare it to the MAP and the Random-OMP method devised for approximating the MMSE result.  ...  In a follow-up work, we intend to implement this estimator on images, with necessary modifications to the model generation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/eeei.2008.4736597">doi:10.1109/eeei.2008.4736597</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/goosk2p25rawncf7dsuxorbci4">fatcat:goosk2p25rawncf7dsuxorbci4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705101845/http://www.cs.technion.ac.il/~elad/publications/conferences/2008/IEEE_08_MMSE.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/bd/94bd3a4a02c4c69065dcdfa555c4db4fb63b3e6f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/eeei.2008.4736597"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Closed-Form MMSE Estimation for Signal Denoising Under Sparse Representation Modeling Over a Unitary Dictionary

Matan Protter, Irad Yavneh, Michael Elad
<span title="">2010</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gkn2pu46ozb4tmkxczacnmtvkq" style="color: black;">IEEE Transactions on Signal Processing</a> </i> &nbsp;
This paper deals with the Bayesian signal denoising problem, assuming a prior based on a sparse representation modeling over a unitary dictionary.  ...  The MAP and MMSE estimators are re-developed for this extended model, again resulting in closed-form simple algorithms.  ...  THE CASE OF A UNITARY DICTIONARY A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2010.2046596">doi:10.1109/tsp.2010.2046596</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a2vpi2xo5rhcjmc732gdqh5dwm">fatcat:a2vpi2xo5rhcjmc732gdqh5dwm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090709155327/http://www.cs.technion.ac.il/~elad/publications/journals/2009/MMSE_Unitary_IEEE_SP.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bb/4a/bb4aacc25db9a74a67f8a5e0aefe191e1daa51f7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2010.2046596"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

MMSE Approximation For Sparse Coding Algorithms Using Stochastic Resonance [article]

Dror Simon, Jeremias Sulam, Yaniv Romano, Yue M. Lu, Michael Elad
<span title="2019-04-11">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The first is a provably convergent approximation to the Minimum Mean Square Error (MMSE) estimator, relying on the generative model and applying a weighted average over the recovered solutions.  ...  From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a sparse prior.  ...  The research leading to these results has received funding from the European Research Council under European Unions Seventh Framework Programme, ERC Grant agreement no. 320649 and the Israel Science Foundation  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1806.10171v5">arXiv:1806.10171v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t7ubtax32jfhnkdbblg7jnvxba">fatcat:t7ubtax32jfhnkdbblg7jnvxba</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200831171211/https://arxiv.org/pdf/1806.10171v5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b2/a6/b2a6f8d4f60bf82be1fbea0e866dd94381a420aa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1806.10171v5" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Denoising of image patches via sparse representations with learned statistical dependencies

Tomer Faktor, Yonina C. Eldar, Michael Elad
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rc5jnc4ldvhs3dswicq5wk3vsq" style="color: black;">2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</a> </i> &nbsp;
In this work we focus on the special case of a unitary dictionary and obtain the exact MAP estimate for the sparse representation using an efficient message passing algorithm.  ...  This adaptive approach is applied on noisy image patches in order to recover their sparse representations over a fixed unitary dictionary.  ...  We consider a signal which is built as = + , where is a unitary dictionary of size -by-, is a sparse representation over this dictionary and is additive white Gaussian noise with variance 2 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icassp.2011.5947684">doi:10.1109/icassp.2011.5947684</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icassp/FaktorEE11.html">dblp:conf/icassp/FaktorEE11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pbhgbthtfjaghpe73ae2vuvf24">fatcat:pbhgbthtfjaghpe73ae2vuvf24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809050953/http://webee.technion.ac.il/Sites/People/YoninaEldar/Denoising.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e7/82/e7821b16d7d771fa23c13d01bf99bd7a022b12cb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icassp.2011.5947684"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Partially Linear Estimation with Application to Image Deblurring Using Blurred/Noisy Image Pairs [chapter]

Tomer Michaeli, Daniel Sigalov, Yonina C. Eldar
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We demonstrate the utility of PLMMSE estimation in recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version of it.  ...  We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y .  ...  Application to Sparse Approximations Consider the situation in which X is known to be sparsely representable in a unitary dictionary Ψ ∈ R M ×M in the sense that X = Ψ A (7) for some RV A that is sparse  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-28551-6_2">doi:10.1007/978-3-642-28551-6_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nxd7ebyvlvdvtj2qo5z7nzzb7e">fatcat:nxd7ebyvlvdvtj2qo5z7nzzb7e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20131017175753/http://webee.technion.ac.il/people/YoninaEldar/conferences/main_plmmse_lva.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d4/cc/d4cc4baa4fe0cd78dcb2373163fea2f567a2f82e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-28551-6_2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Partially Linear Estimation With Application to Sparse Signal Recovery From Measurement Pairs

Tomer Michaeli, Daniel Sigalov, Yonina C. Eldar
<span title="">2012</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gkn2pu46ozb4tmkxczacnmtvkq" style="color: black;">IEEE Transactions on Signal Processing</a> </i> &nbsp;
We demonstrate our approach in the context of recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version of it.  ...  We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of X and Y.  ...  In Section IV, we derive the PLMMSE estimator for recovering a signal, sparse in a unitary dictionary, from a pair of observations, one blurred and one noisy.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2012.2185232">doi:10.1109/tsp.2012.2185232</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ru6cuke4qzcexgneqdb6ri4rzi">fatcat:ru6cuke4qzcexgneqdb6ri4rzi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808195736/http://www.wisdom.weizmann.ac.il/~tomermic/papers/PLMMSE.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6e/13/6e131ce01f54f7dc507e6e5746706b09f3f5b6ba.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2012.2185232"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Exploiting Statistical Dependencies in Sparse Representations for Signal Recovery

Tomer Peleg, Yonina C. Eldar, Michael Elad
<span title="">2012</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gkn2pu46ozb4tmkxczacnmtvkq" style="color: black;">IEEE Transactions on Signal Processing</a> </i> &nbsp;
We then consider a special case in which exact MAP is feasible, by assuming that the dictionary is unitary and the dependency model corresponds to a certain sparse graph.  ...  For general dependency models, exact MAP and MMSE estimation of the sparse representation becomes computationally complex.  ...  These results correspond to those of [15] for the MAP estimator under a unitary dictionary.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2012.2188520">doi:10.1109/tsp.2012.2188520</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b2z3kvttdbh5jmqcire22qsuhe">fatcat:b2z3kvttdbh5jmqcire22qsuhe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808043537/http://webee.technion.ac.il/Sites/People/YoninaEldar/Info/Exploiting%20Statistical%20Dependencies%20in%20Sparse.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/dc/57dcea23e210292073de7256f6084f1d95dc2aa1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2012.2188520"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

A Statistical Prediction Model Based on Sparse Representations for Single Image Super-Resolution

Tomer Peleg, Michael Elad
<span title="">2014</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dhlhr4jqkbcmdbua2ca45o7kru" style="color: black;">IEEE Transactions on Image Processing</a> </i> &nbsp;
We address single image super-resolution using a statistical prediction model based on sparse representations of low and high resolution image patches.  ...  We suggest a training scheme for the resulting network and demonstrate the capabilities of our algorithm, showing its advantages over existing methods based on a low and high resolution dictionary pair  ...  assumption of sparse representation invariance over a low and high resolution dictionary pair.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tip.2014.2305844">doi:10.1109/tip.2014.2305844</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24815620">pmid:24815620</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qqmf2fzlrbdbbj3svy7siw5k3i">fatcat:qqmf2fzlrbdbbj3svy7siw5k3i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20161124072315/http://www.cs.technion.ac.il/~elad/publications/journals/2013/SingleImageSR_TIP.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f4/8d/f48d7f8a62ab2acc1c769b60c26ba338525d9ffd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tip.2014.2305844"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Joint Prior Learning for Visual Sensor Network Noisy Image Super-Resolution

Bo Yue, Shuang Wang, Xuefeng Liang, Licheng Jiao, Caijin Xu
<span title="2016-02-26">2016</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/taedaf6aozg7vitz5dpgkojane" style="color: black;">Sensors</a> </i> &nbsp;
Unlike conventional methods that only focus on upscaling images, JPISR alternatively solves upscaling mapping and denoising in the E-step and M-step.  ...  Moreover, JPISR does not rely on large external datasets for training, which is much more practical in a VSN.  ...  Author Contributions: Bo Yue proposed the original algorithm and wrote this paper; Shuang Wang and Xuefeng Liang revisited the paper and supervised a whole process; Licheng Jiao and Caijin Xu gave some  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/s16030288">doi:10.3390/s16030288</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26927114">pmid:26927114</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4813863/">pmcid:PMC4813863</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5fx6qwhkljhfdmnuuwpkdcqq4y">fatcat:5fx6qwhkljhfdmnuuwpkdcqq4y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190418152447/https://core.ac.uk/download/pdf/39335691.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f5/64/f564f7a0db0fe039f59288fb21399e186bd287eb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/s16030288"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4813863" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Analytics of Unconstrained Convex Problems in Sparse and Redundant Representations: A Case Study on Image Processing Applications

Pooja Patil, Subhash S.
<span title="2019-07-17">2019</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
The key objective of sparse and redundant representations is all about the introduction of a highly elegant data model with well-defined mathematical foundations.  ...  The appeal of this model is attributed to compact representation it facilitates. A lot of freedom persists in model adaptation to fit the data depending on the application.  ...  In this context, from image processing perspective, the sparse model is based on the assumption that a given image has a sparse representation w.r.t. a specific redundant dictionary A which is described  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/ijca2019919223">doi:10.5120/ijca2019919223</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nyuxhdaf75bbvmowdxa7wnpbqi">fatcat:nyuxhdaf75bbvmowdxa7wnpbqi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200709025204/https://www.ijcaonline.org/archives/volume178/number34/patil-2019-ijca-919223.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0d/be/0dbe61ea27c2cb1d30dc23a0a0f711c80bc13470.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/ijca2019919223"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond [article]

Zhishen Huang and Siqi Ye and Michael T. McCann and Saiprasad Ravishankar
<span title="2021-03-26">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This review includes many recent methods based on unsupervised learning, and supervised learning, as well as a framework to combine multiple types of learned models together.  ...  These methods include synthesis dictionary learning, sparsifying transform learning, and different forms of deep learning involving complex neural networks.  ...  There is theoretical justification for this: even though (18) is a denoising problem, the effective noise may not be Gaussian and the formulation suggests that a MAP rather than MMSE denoiser is required  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.14528v1">arXiv:2103.14528v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kxzugqnnijdwfn62jwrl45zmge">fatcat:kxzugqnnijdwfn62jwrl45zmge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210330001814/https://arxiv.org/pdf/2103.14528v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/23/f8/23f841392570f0024a528f5335cc0f6d49969f2a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.14528v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Statistical limits of dictionary learning: random matrix theory and the spectral replica method [article]

Jean Barbier, Nicolas Macris
<span title="2022-02-26">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with  ...  Next, we analyze the more challenging models of dictionary learning.  ...  Foini, A. Maillard, M. Mézard, F. Krzakala and L. Zdeborová for discussions and pointing out the problematic issues with the replica ansatz in [55] . J.B. also thanks A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.06610v4">arXiv:2109.06610v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/54ajz37i3zc3he2zumluov5ztu">fatcat:54ajz37i3zc3he2zumluov5ztu</a> </span>
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Hyperspectral and Multispectral Image Fusion based on a Sparse Representation [article]

Qi Wei, José Bioucas-Dias, Nicolas Dobigeon, Jean-Yves Tourneret
<span title="2014-09-19">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A sparse regularization term is carefully designed, relying on a decomposition of the scene on a set of dictionaries.  ...  Then, conditionally on these dictionaries and supports, the fusion problem is solved via alternating optimization with respect to the target image (using the alternating direction method of multipliers  ...  Paul Scheunders and Dr. Yifan Zhang for sharing the codes of [20] , Dr. Naoto Yokoya for sharing the codes of [23] and Jordi Inglada, from Centre National d'Études  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1409.5729v1">arXiv:1409.5729v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5logwcrw6zauhhgsuch5eyf6lq">fatcat:5logwcrw6zauhhgsuch5eyf6lq</a> </span>
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Hyperspectral and Multispectral Image Fusion Based on a Sparse Representation

Qi Wei, Jose Bioucas-Dias, Nicolas Dobigeon, Jean-Yves Tourneret
<span title="">2015</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4odsbtjobjalfki6xxabjpdu6y" style="color: black;">IEEE Transactions on Geoscience and Remote Sensing</a> </i> &nbsp;
A sparse regularization term is carefully designed, relying on a decomposition of the scene on a set of dictionaries.  ...  Index Terms-Alternating direction method of multipliers (ADMM), dictionary, hyperspectral (HS) image, image fusion, multispectral (MS) image, sparse representation.  ...  Scheunders and Dr. Y. Zhang for sharing the codes of [17] , Dr. N. Yokoya for sharing the codes of [18] , Prof. P. Gamba for providing the ROSIS data over Pavia, and J.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tgrs.2014.2381272">doi:10.1109/tgrs.2014.2381272</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c5jejcz4r5dkrnr5uel5mtbnra">fatcat:c5jejcz4r5dkrnr5uel5mtbnra</a> </span>
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