[
{
"id": "authors:wbj75-1gv55",
"collection": "authors",
"collection_id": "wbj75-1gv55",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220307-188412000",
"type": "book_section",
"title": "Inference of Black Hole Fluid-Dynamics from Sparse Interferometric Measurements",
"book_title": "2021 IEEE/CVF International Conference on Computer Vision (ICCV)",
"author": [
{
"family_name": "Levis",
"given_name": "Aviad",
"orcid": "0000-0001-7307-632X",
"clpid": "Levis-Aviad"
},
{
"family_name": "Lee",
"given_name": "Daeyoung",
"clpid": "Lee-Daeyoung"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Gammie",
"given_name": "Charles F.",
"orcid": "0000-0001-7451-8935",
"clpid": "Gammie-Charles-F"
},
{
"family_name": "Bouman",
"given_name": "Katherine L.",
"orcid": "0000-0003-0077-4367",
"clpid": "Bouman-K-L"
}
],
"abstract": "We develop an approach to recover the underlying properties of fluid-dynamical processes from sparse measurements. We are motivated by the task of imaging the stochastically evolving environment surrounding black holes, and demonstrate how flow parameters can be estimated from sparse interferometric measurements used in radio astronomical imaging. To model the stochastic flow we use spatio-temporal Gaussian Random Fields (GRFs). The high dimensionality of the underlying source video makes direct representation via a GRF's full covariance matrix intractable. In contrast, stochastic partial differential equations are able to capture correlations at multiple scales by specifying only local interaction coefficients. Our approach estimates the coefficients of a space-time diffusion equation that dictates the stationary statistics of the dynamical process. We analyze our approach on realistic simulations of black hole evolution and demonstrate its advantage over state-of-the-art dynamic black hole imaging techniques.",
"doi": "10.1109/iccv48922.2021.00234",
"isbn": "978-1-6654-2812-5",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2021-10",
"pages": "2320-2329"
},
{
"id": "authors:xgnz6-yxr86",
"collection": "authors",
"collection_id": "xgnz6-yxr86",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200821-083421883",
"type": "book_section",
"title": "Concentration of the Intrinsic Volumes of a Convex Body",
"book_title": "Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2017-2019 Volume II",
"author": [
{
"family_name": "Lotz",
"given_name": "Martin",
"orcid": "0000-0001-8500-864X",
"clpid": "Lotz-Martin"
},
{
"family_name": "McCoy",
"given_name": "Michael B.",
"clpid": "McCoy-Michael-B"
},
{
"family_name": "Nourdin",
"given_name": "Ivan",
"orcid": "0000-0002-8742-0723",
"clpid": "Nourdin-Ivan"
},
{
"family_name": "Peccati",
"given_name": "Giovanni",
"clpid": "Peccati-Giovanni"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"contributor": [
{
"family_name": "Klartag",
"given_name": "Bo'az",
"clpid": "Klartag-Bo'az"
},
{
"family_name": "Milman",
"given_name": "Emanuel",
"clpid": "Milman-Emanuel"
}
],
"abstract": "The intrinsic volumes are measures of the content of a convex body. This paper applies probabilistic and information-theoretic methods to study the sequence of intrinsic volumes. The main result states that the intrinsic volume sequence concentrates sharply around a specific index, called the central intrinsic volume. Furthermore, among all convex bodies whose central intrinsic volume is fixed, an appropriately scaled cube has the intrinsic volume sequence with maximum entropy.",
"doi": "10.1007/978-3-030-46762-3_6",
"isbn": "978-3-030-46761-6",
"publisher": "Springer",
"place_of_publication": "Cham",
"publication_date": "2020-07-09",
"pages": "139-167"
},
{
"id": "authors:ejhk7-npe53",
"collection": "authors",
"collection_id": "ejhk7-npe53",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190826-161640394",
"type": "book_section",
"title": "Sketchy decisions: convex optimization with optimal storage (Conference Presentation)",
"book_title": "Wavelets and Sparsity XVII",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"contributor": [
{
"family_name": "Lu",
"given_name": "Yue M.",
"clpid": "Lu-Yue-M"
},
{
"family_name": "Van De Ville",
"given_name": "Dimitri",
"clpid": "Van-De-Ville-D"
},
{
"family_name": "Papadakis",
"given_name": "Manos",
"clpid": "Papadakis-M"
}
],
"abstract": "This recording is for the presentation titled, \"Sketchy decisions: convex optimization with optimal storage\", part of the SPIE symposium on \"SPIE Optical Engineering + Applications\"",
"doi": "10.1117/12.2281058",
"isbn": "9781510612457",
"publisher": "Society of Photo-Optical Instrumentation Engineers (SPIE)",
"place_of_publication": "Bellingham, WA",
"publication_date": "2017-09-22",
"pages": "Art. No. 1039403"
},
{
"id": "authors:bemq2-qw914",
"collection": "authors",
"collection_id": "bemq2-qw914",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170214-075417526",
"type": "book_section",
"title": "The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach",
"book_title": "High Dimensional Probability VII",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"contributor": [
{
"family_name": "Houdr\u00e9",
"given_name": "Christian",
"clpid": "Houdr\u00e9-C"
},
{
"family_name": "Mason",
"given_name": "David M.",
"clpid": "Mason-D-M"
},
{
"family_name": "Reynaud-Bouret",
"given_name": "Patricia",
"clpid": "Reynaud-Bouret-P"
},
{
"family_name": "Rosi\u0144ski",
"given_name": "Jan",
"clpid": "Rosi\u0144ski-J"
}
],
"abstract": "In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the random matrix and the expectation of the maximum squared norm achieved by one of the summands; there is also a weak dependence on the dimension of the random matrix. The purpose of this paper is to give a complete, elementary proof of this important inequality.",
"doi": "10.1007/978-3-319-40519-3_8",
"isbn": "978-3-319-40517-9",
"publisher": "Springer",
"place_of_publication": "Cham",
"publication_date": "2016-09-22",
"pages": "173-202"
},
{
"id": "authors:1vmc9-r4269",
"collection": "authors",
"collection_id": "1vmc9-r4269",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160818-084011981",
"type": "book_section",
"title": "Convex Recovery of a Structured Signal from Independent Random Linear Measurements",
"book_title": "Sampling Theory, a Renaissance: Compressive Sensing and Other Developments",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"contributor": [
{
"family_name": "Pfander",
"given_name": "G\u00f6tz E.",
"clpid": "Pfander-G-E"
}
],
"abstract": "This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar to recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the chapter presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.",
"doi": "10.1007/978-3-319-19749-4_2",
"isbn": "978-3-319-19748-7",
"publisher": "Springer",
"place_of_publication": "Cham, Switzerland",
"publication_date": "2015",
"pages": "67-101"
},
{
"id": "authors:ez84w-x7c72",
"collection": "authors",
"collection_id": "ez84w-x7c72",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160401-170735760",
"type": "book_section",
"title": "Time\u2013Data Tradeoffs by Aggressive Smoothing",
"author": [
{
"family_name": "Bruer",
"given_name": "John J.",
"clpid": "Bruer-J-J"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Cevher",
"given_name": "Volkan",
"clpid": "Cevher-V"
},
{
"family_name": "Becker",
"given_name": "Stephen R.",
"clpid": "Becker-S-R"
}
],
"contributor": [
{
"family_name": "Ghahramani",
"given_name": "Z.",
"clpid": "Ghahramani-Z"
},
{
"family_name": "Welling",
"given_name": "M.",
"clpid": "Welling-M"
},
{
"family_name": "Cortes",
"given_name": "C.",
"clpid": "Cortes-C"
},
{
"family_name": "Lawrence",
"given_name": "N. D.",
"clpid": "Lawrence-N-D"
},
{
"family_name": "Weinberger",
"given_name": "K. Q.",
"clpid": "Weinberger-K-Q"
}
],
"abstract": "This paper proposes a tradeoff between sample complexity and computation time that applies to statistical estimators based on convex optimization. As the amount of\ndata increases, we can smooth optimization problems more and more aggressively to achieve accurate estimates more quickly. This work provides theoretical and\nexperimental evidence of this tradeoff for a class of regularized linear inverse problems.",
"publisher": "Neural Information Processing Systems",
"publication_date": "2014"
},
{
"id": "authors:4tr2r-xse68",
"collection": "authors",
"collection_id": "4tr2r-xse68",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160401-165447853",
"type": "book_section",
"title": "Factoring nonnegative matrices with linear programs",
"book_title": "Advances in Neural Information Processing Systems 25 (NIPS 2012)",
"author": [
{
"family_name": "Bittorf",
"given_name": "Victor",
"clpid": "Bittorf-V"
},
{
"family_name": "Recht",
"given_name": "Benjamin",
"clpid": "Recht-B"
},
{
"family_name": "R\u00e9",
"given_name": "Christopher",
"clpid": "R\u00e9-C"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"contributor": [
{
"family_name": "Pereira",
"given_name": "F.",
"clpid": "Pereira-F"
},
{
"family_name": "Burges",
"given_name": "C. J. C.",
"clpid": "Burges-C-J-C"
},
{
"family_name": "Bottou",
"given_name": "L.",
"clpid": "Bottou-L"
},
{
"family_name": "Weinberger",
"given_name": "K. Q.",
"clpid": "Weinberger-K-Q"
}
],
"abstract": "This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven\nmodel for the factorization where the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm\nidentifies a matrix C that satisfies X \u2248 CX and some linear constraints. The constraints are chosen to ensure that the matrix C selects features; these features can then be used to find a low-rank NMF of X. A theoretical analysis\ndemonstrates that this approach has guarantees similar to those of the recent NMF algorithm of Arora et al. (2012). In contrast with this earlier work, the proposed\nmethod extends to more general noise models and leads to efficient, scalable algorithms. Experiments with synthetic and real datasets provide evidence that the\nnew approach is also superior in practice. An optimized C++ implementation can factor a multigigabyte matrix in a matter of minutes.",
"doi": "10.48550/arXiv.1206.1270",
"isbn": "978-1-62748-003-1",
"publisher": "Neural Information Processing Systems",
"place_of_publication": "La Jolla, CA",
"publication_date": "2012"
},
{
"id": "authors:sm6cv-f2606",
"collection": "authors",
"collection_id": "sm6cv-f2606",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180831-112116678",
"type": "book_section",
"title": "The sparsity gap: Uncertainty principles proportional to dimension",
"book_title": "2010 44th Annual Conference on Information Sciences and Systems (CISS)",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"abstract": "In an incoherent dictionary, most signals that admit a sparse representation admit a unique sparse representation. In other words, there is no way to express the signal without using strictly more atoms. This work demonstrates that sparse signals typically enjoy a higher privilege: each nonoptimal representation of the signal requires far more atoms than the sparsest representation-unless it contains many of the same atoms as the sparsest representation. One impact of this finding is to confer a certain degree of legitimacy on the particular atoms that appear in a sparse representation. This result can also be viewed as an uncertainty principle for random sparse signals over an incoherent dictionary.",
"doi": "10.1109/CISS.2010.5464824",
"isbn": "978-1-4244-7416-5",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2010-03",
"pages": "1-6"
},
{
"id": "authors:bcew3-g2m51",
"collection": "authors",
"collection_id": "bcew3-g2m51",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160331-164724199",
"type": "book_section",
"title": "Practical Large-Scale Optimization for Max-Norm Regularization",
"book_title": "Advances in Neural Information Processing Systems 23",
"author": [
{
"family_name": "Lee",
"given_name": "Jason",
"clpid": "Lee-J"
},
{
"family_name": "Recht",
"given_name": "Benjamin",
"clpid": "Recht-B"
},
{
"family_name": "Salakhutdinov",
"given_name": "Ruslan R.",
"clpid": "Salakhutdinov-R-R"
},
{
"family_name": "Srebro",
"given_name": "Nathan",
"clpid": "Srebro-N"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"contributor": [
{
"family_name": "Lafferty",
"given_name": "J. D.",
"clpid": "Lafferty-J-D"
},
{
"family_name": "Williams",
"given_name": "C. K. I.",
"clpid": "Williams-C-K-I"
},
{
"family_name": "Shawe-Taylor",
"given_name": "John",
"clpid": "Shawe-Taylor-J"
},
{
"family_name": "Zemel",
"given_name": "R. S.",
"clpid": "Zemel-R-S"
},
{
"family_name": "Culotta",
"given_name": "A.",
"clpid": "Culotta-A"
}
],
"abstract": "The max-norm was proposed as a convex matrix regularizer in [1] and was shown to be empirically superior to the trace-norm for collaborative filtering problems.\nAlthough the max-norm can be computed in polynomial time, there are currently no practical algorithms for solving large-scale optimization problems that incorporate\nthe max-norm. The present work uses a factorization technique of Burer and Monteiro [2] to devise scalable first-order algorithms for convex programs\ninvolving the max-norm. These algorithms are applied to solve huge collaborative filtering, graph cut, and clustering problems. Empirically, the new methods\noutperform mature techniques from all three areas.",
"isbn": "9781617823800",
"publisher": "Neural Information Processing Systems",
"place_of_publication": "La Jolla, CA",
"publication_date": "2010"
},
{
"id": "authors:1kq65-m1r89",
"collection": "authors",
"collection_id": "1kq65-m1r89",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100921-101535590",
"type": "book_section",
"title": "Column Subset Selection, Matrix Factorization, and Eigenvalue Optimization",
"book_title": "Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"contributor": [
{
"family_name": "Mathieu",
"given_name": "Claire",
"clpid": "Mathieu-C"
}
],
"abstract": "Given a fixed matrix, the problem of column subset selection\nrequests a column submatrix that has favorable spectral\nproperties. Most research from the algorithms and\nnumerical linear algebra communities focuses on a variant\ncalled rank-revealing QR, which seeks a well-conditioned\ncollection of columns that spans the (numerical) range of\nthe matrix. The functional analysis literature contains\nanother strand of work on column selection whose algorithmic\nimplications have not been explored. In particular,\na celebrated result of Bourgain and Tzafriri demonstrates\nthat each matrix with normalized columns contains\na large column submatrix that is exceptionally well\nconditioned. Unfortunately, standard proofs of this result\ncannot be regarded as algorithmic. This paper presents\na randomized, polynomial-time algorithm that produces\nthe submatrix promised by Bourgain and Tzafriri. The\nmethod involves random sampling of columns, followed by\na matrix factorization that exposes the well-conditioned\nsubset of columns. This factorization, which is due to\nGrothendieck, is regarded as a central tool in modern\nfunctional analysis. The primary novelty in this work\nis an algorithm, based on eigenvalue minimization, for\nconstructing the Grothendieck factorization. These ideas\nalso result in an approximation algorithm for the (\u221e, 1)\nnorm of a matrix, which is generally NP-hard to compute\nexactly. As an added bonus, this work reveals a surprising\nconnection between matrix factorization and the famous\nmaxcut semidefinite program.",
"doi": "10.48550/arXiv.0806.4404",
"isbn": "978-0-898716-80-1",
"publisher": "Association for Computing Machinery",
"place_of_publication": "New York",
"publication_date": "2009",
"pages": "978-986"
},
{
"id": "authors:mrem4-vrd44",
"collection": "authors",
"collection_id": "mrem4-vrd44",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180831-112113124",
"type": "book_section",
"title": "Efficient Sampling of Sparse Wideband Analog Signals",
"book_title": "2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel",
"author": [
{
"family_name": "Mishali",
"given_name": "Moshe",
"clpid": "Mishali-M"
},
{
"family_name": "Eldar",
"given_name": "Yonina C.",
"clpid": "Eldar-Y-C"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"abstract": "Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This assumption becomes impractical for wideband sparse signals. The current paper proposes an alternative sampling stage that does not require a full-band front end. Instead, signals are captured with an analog front end that consists of a bank of multipliers and lowpass filters whose cutoff is much lower than the Nyquist rate. The problem of recovering the original signal from the low-rate samples can be studied within the framework of compressive sampling. An appropriate parameter selection ensures that the samples uniquely determine the analog input. Moreover, the analog input can be stably reconstructed with digital algorithms. Numerical experiments support the theoretical analysis.",
"doi": "10.1109/EEEI.2008.4736707",
"isbn": "978-1-4244-2481-8",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2008-12",
"pages": "290-294"
},
{
"id": "authors:j70zc-y3276",
"collection": "authors",
"collection_id": "j70zc-y3276",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180831-112109709",
"type": "book_section",
"title": "Greedy Signal Recovery Review",
"book_title": "2008 42nd Asilomar Conference on Signals, Systems and Computers",
"author": [
{
"family_name": "Needell",
"given_name": "Deanna",
"orcid": "0000-0002-8058-8638",
"clpid": "Needell-Deanna"
},
{
"family_name": "Tropp",
"given_name": "Joel",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Vershynin",
"given_name": "Roman",
"clpid": "Vershynin-R"
}
],
"abstract": "The two major approaches to sparse recovery are L_1-minimization and greedy methods. Recently, Needell and Vershynin developed regularized orthogonal matching pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees. \n\nEven more recently, Needell and Tropp developed the stable greedy algorithm compressive sampling matching pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(N log N), where N is the ambient dimension of the signal. This review summarizes these major advances.",
"doi": "10.1109/ACSSC.2008.5074572",
"isbn": "978-1-4244-2941-7",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2008-10",
"pages": "1048-1050"
},
{
"id": "authors:sf41z-mfp58",
"collection": "authors",
"collection_id": "sf41z-mfp58",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TROciss06.975",
"type": "book_section",
"title": "Random Filters for Compressive Sampling",
"book_title": "Conference on Information Sciences and Systems, 40th (CISS 2006), Princeton, NJ, 22-24 March 2006",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"abstract": "This paper discusses random filtering, a recently proposed method for directly acquiring a compressed version of a digital signal. The technique is based on convolution of the signal with a fixed FIR filter having random taps, followed by downsampling. Experiments show that random filtering is effective at acquiring sparse and compressible signals. This process has the potential for implementation in analog hardware, and so it may have a role to play in new types of analog/digital converters.",
"doi": "10.1109/CISS.2006.286465",
"isbn": "1-4244-0350-2",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2007-01-22",
"pages": "216-217"
},
{
"id": "authors:900p1-ymh12",
"collection": "authors",
"collection_id": "900p1-ymh12",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SRAicassp06.963",
"type": "book_section",
"title": "Row-Action Methods for Compressed Sensing",
"book_title": "International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, 14-19 May 2006",
"author": [
{
"family_name": "Sra",
"given_name": "Suvrit",
"clpid": "Sra-S"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"abstract": "Compressed Sensing uses a small number of random, linear measurements to acquire a sparse signal. Nonlinear algorithms, such as l1minimization, are used to reconstruct the signal from the measured data. This paper proposes row-action methods as a computational approach to solving the l1optimization problem. This paper presents a specific row-action method and provides extensive empirical evidence that it is an effective technique for signal reconstruction. This approach offers several advantages over interior-point methods, including minimal storage and computational requirements, scalability, and robustness.",
"doi": "10.1109/ICASSP.2006.1660792",
"isbn": "1-4244-0469-X",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2006-07-24",
"pages": "III-868"
},
{
"id": "authors:hp8sm-g0q87",
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"collection_id": "hp8sm-g0q87",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TROicassp06.977",
"type": "book_section",
"title": "Random Filters for Compressive Sampling and Reconstruction",
"book_title": "International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, 14-19 May 2006",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Wakin",
"given_name": "Michael .",
"clpid": "Wakin-M-B"
},
{
"family_name": "Duarte",
"given_name": "Marco F.",
"clpid": "Duarte-M-F"
},
{
"family_name": "Baron",
"given_name": "Dror",
"clpid": "Baron-D"
},
{
"family_name": "Baraniuk",
"given_name": "Richard G.",
"orcid": "0000-0002-0721-8999",
"clpid": "Baraniuk-R-G"
}
],
"abstract": "We propose and study a new technique for efficiently acquiring and reconstructing signals based on convolution with a fixed FIR filter having random taps. The method is designed for sparse and compressible signals, i.e., ones that are well approximated by a short linear combination of vectors from an orthonormal basis. Signal reconstruction involves a non-linear Orthogonal Matching Pursuit algorithm that we implement efficiently by exploiting the nonadaptive, time-invariant structure of the measurement process. While simpler and more efficient than other random acquisition techniques like Compressed Sensing, random filtering is sufficiently generic to summarize many types of compressible signals and generalizes to streaming and continuous-time signals. Extensive numerical experiments demonstrate its efficacy for acquiring and reconstructing signals sparse in the time, frequency, and wavelet domains, as well as piecewise smooth signals and Poisson processes.",
"doi": "10.1109/ICASSP.2006.1660793",
"isbn": "1-4244-0469-X",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2006-07-24",
"pages": "III-872"
},
{
"id": "authors:5gpyq-hz670",
"collection": "authors",
"collection_id": "5gpyq-hz670",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:HERicassp06.876",
"type": "book_section",
"title": "Sparse Approximation Via Iterative Thresholding",
"book_title": "International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, 14-19 May 2006",
"author": [
{
"family_name": "Herrity",
"given_name": "Kyle K.",
"clpid": "Herrity-K-K"
},
{
"family_name": "Gilbert",
"given_name": "Anna C.",
"clpid": "Gilbert-A-C"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"abstract": "The well-known shrinkage technique is still relevant for contemporary signal processing problems over redundant dictionaries. We present theoretical and empirical analyses for two iterative algorithms for sparse approximation that use shrinkage. The GENERAL IT algorithm amounts to a Landweber iteration with nonlinear shrinkage at each iteration step. The BLOCK IT algorithm arises in morphological components analysis. A sufficient condition for which General IT exactly recovers a sparse signal is presented, in which the cumulative coherence function naturally arises. This analysis extends previous results concerning the Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) algorithms to IT algorithms.",
"doi": "10.1109/ICASSP.2006.1660731",
"isbn": "1-4244-0469-X",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2006-07-24",
"pages": "III-624"
},
{
"id": "authors:yhdsp-53481",
"collection": "authors",
"collection_id": "yhdsp-53481",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:GILisit05",
"type": "book_section",
"title": "Applications of sparse approximation in communications",
"book_title": "International Symposium on Information Theory (ISIT '05), Adelaide, Australia, 4-9 September 2005",
"author": [
{
"family_name": "Gilbert",
"given_name": "A. C.",
"clpid": "Gilbert-A-C"
},
{
"family_name": "Tropp",
"given_name": "J. A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
}
],
"abstract": "Sparse approximation problems abound in many scientific, mathematical, and engineering applications. These problems are defined by two competing notions: we approximate a signal vector as a linear combination of elementary atoms and we require that the approximation be both as accurate and as concise as possible. We introduce two natural and direct applications of these problems and algorithmic solutions in communications. We do so by constructing enhanced codebooks from base codebooks. We show that we can decode these enhanced codebooks in the presence of Gaussian noise. For MIMO wireless communication channels, we construct simultaneous sparse approximation problems and demonstrate that our algorithms can both decode the transmitted signals and estimate the channel parameters.",
"doi": "10.1109/ISIT.2005.1523488",
"isbn": "0-7803-9151-9",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2005-10-31",
"pages": "1000-1004"
},
{
"id": "authors:22hc7-s3g15",
"collection": "authors",
"collection_id": "22hc7-s3g15",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TROicassp05",
"type": "book_section",
"title": "Simultaneous sparse approximation via greedy pursuit",
"book_title": "IEEE International Conference on Acoustic, Speech, and Signal Processing (ICASSP '05), Philadelphia, PA, 18-23 March 2005",
"author": [
{
"family_name": "Tropp",
"given_name": "J. A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Gilbert",
"given_name": "A. C.",
"clpid": "Gilbert-A-C"
},
{
"family_name": "Strauss",
"given_name": "M. J.",
"clpid": "Strauss-M-J"
}
],
"abstract": "A simple sparse approximation problem requests an approximation of a given input signal as a linear combination of T elementary signals drawn from a large, linearly dependent collection. An important generalization is simultaneous sparse approximation. Now one must approximate several input signals at once using different linear combinations of the same T elementary signals. This formulation appears, for example, when analyzing multiple observations of a sparse signal that have been contaminated with noise. A new approach to this problem is presented here: a greedy pursuit algorithm called simultaneous orthogonal matching pursuit. The paper proves that the algorithm calculates simultaneous approximations whose error is within a constant factor of the optimal simultaneous approximation error. This result requires that the collection of elementary signals be weakly correlated, a property that is also known as incoherence. Numerical experiments demonstrate that the algorithm often succeeds, even when the inputs do not meet the hypotheses of the proof.",
"doi": "10.1109/ICASSP.2005.1416405",
"isbn": "0-7803-8874-7",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2005-05-09",
"pages": "V-721"
},
{
"id": "authors:g9q7e-wkc24",
"collection": "authors",
"collection_id": "g9q7e-wkc24",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TROissta04",
"type": "book_section",
"title": "Optimal CDMA signatures: a finite-step approach",
"book_title": "International Symposium on Spread Spectrum Techniques and Applications, 8th, Sydney, Australia, 30 August - 2 September 2004",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Dhillon",
"given_name": "Inderjit S.",
"clpid": "Dhillon-I-S"
},
{
"family_name": "Heath",
"given_name": "Robert W., Jr.",
"clpid": "Heath-R-W-Jr"
}
],
"abstract": "A description of optimal sequences for direct-sequence code division multiple access is a byproduct of recent characterizations of the sum capacity. The paper restates the sequence design problem as an inverse singular value problem and shows that it can be solved with finite-step algorithms from matrix analysis. Relevant algorithms are reviewed and a new one-sided construction is proposed that obtains the sequences directly instead of computing the Gram matrix of the optimal signatures.",
"isbn": "0-7803-8408-3",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2005-01-03",
"pages": "335-339"
},
{
"id": "authors:cr2rp-9ma37",
"collection": "authors",
"collection_id": "cr2rp-9ma37",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:HEAissta04",
"type": "book_section",
"title": "Construction of equiangular signatures for synchronous CDMA systems",
"book_title": "International Symposium on Spread Spectrum Techniques and Applications, 8th, Sydney, Australia, 30 August - 2 September 2004",
"author": [
{
"family_name": "Heath",
"given_name": "Robert W., Jr.",
"clpid": "Heath-R-W-Jr"
},
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Dhillon",
"given_name": "Inderjit S.",
"clpid": "Dhillon-I-S"
},
{
"family_name": "Strohmer",
"given_name": "Thomas",
"clpid": "Strohmer-T"
}
],
"abstract": "Welch bound equality (WBE) signature sequences maximize the uplink sum capacity in direct-spread synchronous code division multiple access (CDMA) systems. WBE sequences have a nice interference invariance property that typically holds only when the system is fully loaded, and, to maintain this property, the signature set must be redesigned and reassigned as the number of active users changes. An additional equiangular constraint on the signature set, however, maintains interference invariance. Finding such signatures requires equiangular side constraints to be imposed on an inverse eigenvalue problem. The paper presents an alternating projection algorithm that can design WBE sequences that satisfy equiangular side constraints. The proposed algorithm can be used to find Grassmannian frames as well as equiangular tight frames. Though one projection is onto a closed, but non-convex, set, it is shown that this algorithm converges to a fixed point, and these fixed points are partially characterized.",
"isbn": "0-7803-8408-3",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2005-01-03",
"pages": "708-712"
},
{
"id": "authors:4g88j-99p44",
"collection": "authors",
"collection_id": "4g88j-99p44",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TROasilo03",
"type": "book_section",
"title": "CDMA signature sequences with low peak-to-average-power ratio via alternating projection",
"book_title": "Asilomar Conference on Signals, Systems and Computers, 37th, Pacific Grove, CA, 9-12 November 2003",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Dhillon",
"given_name": "Inderjit S.",
"clpid": "Dhillon-I-S"
},
{
"family_name": "Heath",
"given_name": "Robert W., Jr.",
"clpid": "Heath-R-W-Jr"
},
{
"family_name": "Strohmer",
"given_name": "Thomas",
"clpid": "Strohmer-T"
}
],
"contributor": [
{
"family_name": "Matthews",
"given_name": "Michael B."
}
],
"abstract": "Several algorithms have been proposed to construct optimal signature sequences that maximize the sum capacity of the uplink in a direct-spread synchronous code division multiple access (CDMA) system. These algorithms produce signatures with real-valued or complex-valued entries that generally have a large peak-to-average power ratio (PAR). This paper presents an alternating projection algorithm that can design optimal signature sequences that satisfy PAR side constraints. This algorithm converges to a fixed point, and these fixed points are partially characterized.",
"doi": "10.1109/ACSSC.2003.1291956",
"isbn": "0-7803-8104-1",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2004-05-04",
"pages": "475-479"
},
{
"id": "authors:jck9d-nk170",
"collection": "authors",
"collection_id": "jck9d-nk170",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TROisit03",
"type": "book_section",
"title": "Optimal CDMA signature sequences, inverse eigenvalue problems and alternating minimization",
"book_title": "International Symposium on Information Theory (ISIT '03), Yokohama, Japan, 29 June - 4 July 2003",
"author": [
{
"family_name": "Tropp",
"given_name": "Joel A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Heath",
"given_name": "Robert W., Jr.",
"clpid": "Heath-R-W-Jr"
},
{
"family_name": "Strohmer",
"given_name": "Thomas",
"clpid": "Strohmer-T"
}
],
"abstract": "This paper describes the matrix-theoretic ideas known as Welch-bound-equality sequences or unit-norm tight frames that are used to alternate minimizing the total squared correlation. This paper shows the construction of an optimal signature sequences for the synchronous code-division multiple-access (S-CDMA) channel in the presence of white noise and uniform received powers to solve inverse eigenvalue problems that maximize the sum capacity of the S-CDMA channel.",
"doi": "10.1109/ISIT.2003.1228424",
"isbn": "0-7803-7728-1",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2003-09-15",
"pages": "407"
},
{
"id": "authors:r2p14-c5f08",
"collection": "authors",
"collection_id": "r2p14-c5f08",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TROicip03",
"type": "book_section",
"title": "Improved sparse approximation over quasi-incoherent dictionaries",
"book_title": "International Conference on Image Processing (ICIP '03), Barcelona, Spain, 14-17 September 2003",
"author": [
{
"family_name": "Tropp",
"given_name": "J. A.",
"orcid": "0000-0003-1024-1791",
"clpid": "Tropp-J-A"
},
{
"family_name": "Gilbert",
"given_name": "A. C.",
"clpid": "Gilbert-A-C"
},
{
"family_name": "Muthukrishnan",
"given_name": "S.",
"clpid": "Muthukrishnan-S"
},
{
"family_name": "Strauss",
"given_name": "M. J.",
"clpid": "Strauss-M-J"
}
],
"abstract": "This paper discusses a new greedy algorithm for solving the sparse approximation problem over quasi-incoherent dictionaries. These dictionaries consist of waveforms that are uncorrelated \"on average,\" and they provide a natural generalization of incoherent dictionaries. The algorithm provides strong guarantees on the quality of the approximations it produces, unlike most other methods for sparse approximation. Moreover, very efficient implementations are possible via approximate nearest-neighbor data structures",
"isbn": "0-7803-7750-8",
"publisher": "IEEE",
"place_of_publication": "Piscataway, NJ",
"publication_date": "2003",
"pages": "I-37"
}
]