## Tuesday, January 25, 2011

### CS: The really long post of the week: Lost in Translation, lots of papers and summer jobs

Today we have a really long post but first, I wanted to mention the following:
* Bob's entry on Path-finding back to Copenhagen where he talks about the A* algorithm and greedy algorithm.

Dataset B: Coded Exposure Images using Canon Camera and Ferro-Electric Shutter

 Indoor Toy Train (118 pixel blur) Outdoor Green Taxi (235 pixel blur) Outdoor White Taxi (66 pixel blur) Outdoor Car License Plate (60 pixel blur)

* Three of you kindly pointed out the french newsletter of Matlab came out with a Cleve's corner article on compressed sensing. We mentioned it before but what got my attention is the title "La note de Cleve - une reconstruction « magique » : la détection compressée". I am not happy with the translation because before you do some detection, you really need to acquire a signal, a concept that seems to have been lost on Mathworks France. Translation mishaps are the reason I had asked Emmanuel for a translation of the term before it got to be maimed back into French. It's really Acquisition Comprimee. I have written to the PR firm and to Cleve, Moler the founder of Matworks. Let's see how much time it takes to remove this abomination. In the meantime, Cleve kindly responded with

Thanks.  I agree that Candes is particularly well qualified to make this decision.
-- Cleve

But the newsletter still has the wrong translation, muuuhhh. I like Cleve and his software, but maybe we should call their software Mathlabs or something.

* While we are on the subject of language, I think I should be able to learn Spanish by just reading this introduction to compressed sensing (the whole document is Algoritmos y aplicaciones de Compressive Sensing by María José Díaz Sánchez)  Though, I really need to hear someone speak it. It is fascinating how a domain expertise really allows one to hop back and forth between languages. Maybe we should have a Rosetta stone explaining Compressed Sensing in many languages, including Indonesian.

* Stephane Chretien updated his page to include a code to his recent paper. From  his page:

Sparse recovery with unknown variance: a LASSO-type approach. (with Sebastien Darses) PDF. Submitted. An illustration using NESTAv1.1 of Lemma 5.3 about the support of the LASSO solution can be found here. The results can be checked using the modification of S. Becker and J. Bobin's Matlab code available here.

* Yesterday I mentioned a presentation by Vivek Goyal, Alyson Fletcher, Sundeep Rangan entitled The Optimistic Bayesian: Replica Method Analysis of Compressed Sensing

Now let's get on with the new papers that appeared on various webpages and on arxiv:

The Random Demodulator (RD) and the ModulatedWideband Converter (MWC) are two recently proposed compressed sensing (CS) techniques for the acquisition of continuous-time spectrally-sparse signals. They extend the standard CS paradigm from sampling discrete, finite dimensional signals to sampling continuous and possibly infinite dimensional ones, and thus establish the ability to capture these signals at sub-Nyquist sampling rates. The RD and the MWC have remarkably similar structures (similar block diagrams), but their reconstruction algorithms and signal models strongly differ. To date, few results exist that compare these systems, and owing to the potential impacts they could have on spectral estimation in applications like electromagnetic scanning and cognitive radio, we more fully investigate their relationship in this paper. Specifically, we show that the RD and the MWC are both based on the general concept of random filtering, but that the sampling functions characterising the systems differ significantly. We next demonstrate a previously unreported model sensitivity the MWC has to short duration signals that resembles the known sensitivity the RD has to nonharmonic tones. We also show that block convolution is a fundamental aspect of the MWC, allowing it to successfully sample and reconstruct block-sparse (multiband) signals. This aspect is lacking in the RD, but we use it to propose a new CS based acquisition system for continuous-time signals whose amplitudes are block sparse. The paper includes detailed time and frequency domain analyses of the RD and the MWC that differ, sometimes substantially, from published results.

In this paper, we consider power spectral density estimation of bandlimited, wide-sense stationary signals from sub-Nyquist sampled data. This problem has recently received attention from within the emerging field of cognitive radio for example, and solutions have been proposed that use ideas from compressed sensing and the theory of digital alias-free signal processing. Here we develop a compressed sensing based technique that employs multi-coset sampling and produces multi-resolution power spectral estimates at arbitrarily low average sampling rates. The technique applies to spectrally sparse and nonsparse signals alike, but we show that when the widesense stationary signal is spectrally sparse, compressed sensing is able to enhance the estimator. The estimator does not require signal reconstruction and can be directly obtained from a straightforward application of nonnegative least squares.

Sparse Interactions: Identifying High-Dimensional Multilinear Systems via Compressed Sensing by Bobak Nazer and Robert D. Nowak. The abstract reads:
This paper investigates the problem of identifying sparse multilinear systems. Such systems are characterized by multiplicative interactions between the input variables with sparsity meaning that relatively few of all conceivable interactions are present. This problem is motivated by the study of interactions among genes and proteins in living cells. The goal is to develop a sampling/sensing scheme to identify sparse multilinear systems using as few measurements as possible. We derive bounds on the number of measurements required for perfect reconstruction as a function of the sparsity level. Our results extend the notion of compressed sensing from the traditional notion of (linear) sparsity to more refined notions of sparsity encountered in nonlinear systems. In contrast to the linear sparsity models, in the multilinear case the pattern of sparsity may play a role in the sensing requirements.

Structured sublinear compressive sensing via dense belief propagation by Wei Dai, Olgica Milenkovic, Hoa Vin Pham. The abstract reads:
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with Orthogonal Matching Pursuit (OMP) methods. For more elaborate greedy reconstruction schemes, we propose a new family of dense list decoding belief propagation algorithms, as well as reinforced- and multiple-basis belief propagation algorithms. Our simulation results indicate that reinforced BP CS schemes offer very good complexity-performance tradeoffs for very sparse signal vectors.
This paper presents an average case denoising performance analysis for SP, CoSaMP and IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that it is corrupted by an additive random white Gaussian noise and has a K-sparse representation with respect to a known dictionary D. The proposed analysis is based on the RIP, establishing a near-oracle performance guarantee for each of these algorithms. Similar RIP-based analysis was carried out previously for Dantzig Selector (DS) and Basis Pursuit (BP). Past work also considered a mutual-coherence-based analysis of OMP and thresholding. The performance guarantees developed in this work resemble those obtained for the relaxation-based methods (DS and BP), suggesting that the performance is independent of the sparse representation entries contrast and magnitude which is not true for OMP and thresholding.
Sparse Recovery, Kashin Decomposition and Conic Programming by Alexandre d'Aspremont. The abstract reads:
We produce relaxation bounds on the diameter of arbitrary sections of the l1 ball in R^n. We use these results to test conditions for sparse recovery.
CSSF MIMO RADAR: Low-Complexity Compressive Sensing Based MIMO Radar That Uses Step Frequency by Yao Yu, Athina P. Petropulu, H. Vincent Poor. The abstract reads:
A new approach is proposed, namely CSSF MIMO radar, which applies the technique of step frequency (SF) to compressive sensing (CS) based multi-input multi-output (MIMO) radar. The proposed approach enables high resolution range, angle and Doppler estimation, while transmitting narrowband pulses. The problem of joint angle-Doppler-range estimation is first formulated to fit the CS framework, i.e., as an L1 optimization problem. Direct solution of this problem entails high complexity as it employs a basis matrix whose construction requires discretization of the angle-Doppler-range space. Since high resolution requires fine space discretization, the complexity of joint range, angle and Doppler estimation can be prohibitively high. For the case of slowly moving targets, a technique is proposed that achieves significant complexity reduction by successively estimating angle-range and Doppler in a decoupled fashion and by employing initial estimates obtained via matched filtering to further reduce the space that needs to be digitized. Numerical results show that the combination of CS and SF results in a MIMO radar system that has superior resolution and requires far less data as compared to a system that uses a matched filter with SF.
A Novel Approach for Fast Detection of Multiple Change Points in Linear Models by Xiaoping Shi, Yuehua Wu, Baisuo Jin. The abstract reads:
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived from such an analysis may be misleading. There are rich literatures on change point detection. Although many methods have been proposed for detecting multiple change points, using these methods to find multiple change points in a large sample seems not feasible. In this article, a connection between multiple change point detection and variable selection through a proper segmentation of data sequence is established, and a novel approach is proposed to tackle multiple change point detection problem via the following two key steps: (1) apply the recent advances in consistent variable selection methods such as SCAD, adaptive LASSO and MCP to detect change points; (2) employ a refine procedure to improve the accuracy of change point estimation. Five algorithms are hence proposed, which can detect change points with much less time and more accuracy compared to those in literature. In addition, an optimal segmentation algorithm based on residual sum of squares is given. Our simulation study shows that the proposed algorithms are computationally efficient with improved change point estimation accuracy. The new approach is readily generalized to detect multiple change points in other models such as generalized linear models and nonparametric models.

Peak Reduction and Clipping Mitigation by Compressive Sensing by Ebrahim B. Al-Safadi, Tareq Y. Al-Naffouri. The abstract reads:
This work establishes the design, analysis, and fine-tuning of a Peak-to-Average-Power-Ratio (PAPR) reducing system, based on compressed sensing at the receiver of a peak-reducing sparse clipper applied to an OFDM signal at the transmitter. By exploiting the sparsity of the OFDM signal in the time domain relative to a pre-defined clipping threshold, the method depends on partially observing the frequency content of extremely simple sparse clippers to recover the locations, magnitudes, and phases of the clipped coefficients of the peak-reduced signal. We claim that in the absence of optimization algorithms at the transmitter that confine the frequency support of clippers to a predefined set of reserved-tones, no other tone-reservation method can reliably recover the original OFDM signal with such low complexity.
Afterwards we focus on designing different clipping signals that can embed a priori information regarding the support and phase of the peak-reducing signal to the receiver, followed by modified compressive sensing techniques for enhanced recovery. This includes data-based weighted {\ell} 1 minimization for enhanced support recovery and phase-augmention for homogeneous clippers followed by Bayesian techniques.
We show that using such techniques for a typical OFDM signal of 256 subcarriers and 20% reserved tones, the PAPR can be reduced by approximately 4.5 dB with a significant increase in capacity compared to a system which uses all its tones for data transmission and clips to such levels. The design is hence appealing from both capacity and PAPR reduction aspects.

Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm by Qun Mo, Yi Shen. The abstract reads:
This paper demonstrates theoretically that if the restricted isometry constant $\delta_K$ of the compressed sensing matrix satisfies $$\delta_{K+1} < \frac{1}{\sqrt{K}+1},$$ then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover a signal with $K$ nonzero entries in $K$ iterations. In contrast, matrices are also constructed with restricted isometry constant $$\delta_{K+1} = \frac{1}{\sqrt{K}}$$ such that OMP can not recover $K$-sparse $x$ in $K$ iterations. This result shows that the conjecture given by Dai and Milenkovic is ture.

I am sure they meant True, not ture.

Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements by Vijayaraghavan Thirumalai ; Pascal Frossard. The abstract reads:
The distributed representation of correlated images is an important challenge in applications such as multi-view imaging in camera networks or low complexity video coding. This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or the positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements, which are used for estimation of the correlation between images at decoder. We propose a geometry-based correlation model in order to describe the correlation between pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. These prominent visual features are estimated with a sparse approximation of a reference image by a dictionary of geometric basis functions. The corresponding features in the other images are then identified from the compressed measurements. The correlation model is given by the relative geometric transformations between corresponding features. We thus formulate a regularized optimization problem for the estimation of correspondences where the local transformations between images form a consistent motion or disparity map. Then, we propose an efficient joint reconstruction algorithm that decodes the compressed images such that they stay consistent with the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in video sequences or multi-view data. In addition, the proposed reconstruction strategy provides effective decoding performance that compares advantageously to distributed coding schemes based on disparity or motion learning and to independent coding solution based on JPEG-2000.
Efficient Image Reconstruction Under Sparsity Constraints with Application to MRI and Bioluminescence Tomography by Matthieu Guerquin-Kern, J.-C. Baritaux, Michael Unser. The abstract reads:
Most bioimaging modalities rely on indirect measurements of the quantity under investigation. The image is obtained as the result of an optimization problem involving a physical model of the measurement system. Due to the ill-posedness of the above problem, the impact of the noise on the reconstructed images must be controlled. The recent emphasis in biomedical image reconstruction is on regularization schemes that favor sparse solutions, which renders the optimization problem non-smooth. In this work, we show how step-size adaptation can be used to speed up the most recent multi-step algorithms (e.g. FISTA) employed in sparse image recovery. We present experiments in MRI and Fluorescence Molecular Tomography with specifically tailored step-adaptation strategies. Our results demonstrate the possibility of an order-of-magnitude speed enhancement over state-of-the-art algorithms.

In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted 1 minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into two sets, with entries of each set having a specific probability of being nonzero. We propose a weighted 1 minimization recovery algorithm and analyze its performance using a Grassmann angle approach. We compute explicitly the relationship between the system parameters-the weights, the number of measurements, the size of the two sets, the probabilities of being nonzero- so that when i.i.d. random Gaussian measurement matrices are used, the weighted 1 minimization recovers a randomly selected signal drawn from the considered sparsity model with overwhelming probability as the problem dimension increases. This allows us to compute the optimal weights. We demonstrate through rigorous analysis and simulations that for the case when the support of the signal can be divided into two different subclasses with unequal sparsity fractions, the weighted 1 minimization outperforms the regular `1 minimization substantially. We also generalize our results to signal vectors with an arbitrary number of subclasses for sparsity.

Penalized least squares regression is often used for signal denoising and inverse problems, and is commonly interpreted in a Bayesian framework as a Maximum A Posteriori (MAP) estimator, the penalty function being the negative logarithm of the prior. For example, the widely used quadratic program (with an $\ell^1$ penalty) associated to the LASSO / Basis Pursuit Denoising is very often considered as MAP estimation under a Laplacian prior in the context of additive white Gaussian noise (AWGN) reduction. This paper highlights the fact that, while this is {\em one} possible Bayesian interpretation, there can be other equally acceptable Bayesian interpretations. Therefore, solving a penalized least squares regression problem with penalty $\phi(x)$ need not be interpreted as assuming a prior $C\cdot \exp(-\phi(x))$ and using the MAP estimator. In particular, it is shown that for {\em any} prior $P_X$, the minimum mean square error (MMSE) estimator is the solution of a penalized least square problem with some penalty $\phi(x)$, which can be interpreted as the MAP estimator with the prior $C \cdot \exp(-\phi(x))$. Vice-versa, for {\em certain} penalties $\phi(x)$, the solution of the penalized least squares problem is indeed the MMSE estimator, with a certain prior $P_X$. In general $dP_X(x) \neq C \cdot \exp(-\phi(x))dx$.

Sparsity Equivalence of Anisotropic Decompositions by Gitta Kutyniok. The abstract reads;
Anisotropic decompositions using representation systems such as curvelets, contourlet, or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of functions exhibiting singularities on lower dimensional embedded manifolds. The literature now contains various direct proofs of this fact and of related sparse approximation results. However, it seems quite cumbersome to prove such a canon of results for each system separately, while many of the systems exhibit certain similarities. In this paper, with the introduction of the concept of sparsity equivalence, we aim to provide a framework which allows categorization of the ability for sparse approximations of representation systems. This framework, in particular, enables transferring results on sparse approximations from one system to another. We demonstrate this concept for the example of curvelets and shearlets, and discuss how this viewpoint immediately leads to novel results for both systems.

Behind a paywall:

Automatic Container Code Recognition Using Compressed Sensing Method by Chien-Cheng Tseng and Su-Ling Lee. The abstract reads:
In this paper, an automatic container code recognition method is presented by using compressed sensing (CS). First, the compressed sensing approach which uses the constrained L1 minimization method is reviewed. Then, a general pattern recognition framework based on CS theory is described. Next, the CS recognition method is applied to construct an automatic container code recognition system. Finally, the real-life images provided by trading port of Kaohsiung are used to evaluate the performance of the proposed method.
Here are a list of papers that caught my attention as they werre directly or indirectly related to compressive sensing:

Computational Cameras: Approaches, Benefits and Limits by Shree K. Nayar. The abstract reads:
A computational camera uses a combination of optics and software to produce images that cannot be taken with traditional cameras. In the last decade, computational imaging has emerged as a vibrant field of research. A wide variety of computational cameras have been demonstrated - some designed to achieve new imaging functionalities, and others to reduce the complexity of traditional imaging. In this article, we describe how computational cameras have evolved and present a taxonomy for the technical approaches they use. We explore the benefits and limits of computational imaging, and discuss how it is related to the adjacent and overlapping fields of digital imaging, computational photography and computational image sensors.
We consider a generalization of the classical group testing problem. Let us be given a sample contaminated with a chemical substance. We want to estimate the unknown concentration c of this substance in the sample. There is a threshold indicator which can detect whether the concentration is at least a known threshold. We consider both the case when the threshold indicator does not affect the tested units and the more difficult case when the threshold indicator destroys the tested units. For both cases, we present a family of efficient algorithms each of which achieves a good approximation of c using a small number of tests and of auxiliary resources. Each member of the family provides a different tradeoff between the number of tests and the use of other resources involved by the algorithm. Previously known algorithms for this problem use more tests than most of our algorithms do.

Identification and Classification Problems on Pooling Designs for Inhibitor Models by Huilan Chang, Hong-Bin Chen, Hung-Lin Fu. The abstract reads:

Pooling designs are common tools to efficiently distinguish positive clones from negative clones in clone library screening. In some applications, there is a third type of clones called \inhibitors" whose effect is in a sense to obscure the positive clones in pools. Various inhibitor models have been proposed in the literature. We address the inhibitor problems of designing efficient nonadaptive procedures for both identification and classification problems, and improve previous results in three aspects:
* The algorithm that is used to identify the positive clones works on a more general inhibitor model and has a polynomial-time decoding procedure that recovers the set of positives from the knowledge of the outcomes.
* The algorithm that is used to classify all clones works in one-stage, i.e., all tests are arranged in advance without knowing the outcomes of other tests, along with a polynomial-time decoding procedure.
We extend our results to pooling designs on complexes where the property to be screened is defined on subsets of biological objects, instead of on individual ones.

Group testing is a search paradigm where one is given a population [Formula: see text] of n elements and an unknown subset [Formula: see text] of defective elements and the goal is to determine [Formula: see text] by performing tests on subsets of [Formula: see text]. In classical group testing a test on a subset [Formula: see text] receives a YES response if [Formula: see text], and a NO response otherwise. In group testing with inhibitors (GTI), identifying the defective items is more difficult due to the presence of elements called inhibitors that interfere with the queries so that the answer to a query is YES if and only if the queried group contains at least one defective item and no inhibitor. In the present article, we consider a new generalization of the GTI model in which there are two unknown thresholds h and g and the response to a test is YES both in the case when the queried subset contains at least one defective item and less than h inhibitors, and in the case when the queried subset contains at least g defective items. Moreover, our search model assumes that no knowledge on the number [Formula: see text] of defective items is given. We derive lower bounds on the minimum number of tests required to determine the defective items under this model and present an algorithm that uses an almost optimal number of tests.

This paper studies the "explanation problem" for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional tree-ordered case. In this paper, one is given a matrix A whose rows and columns have semantics: special subsets of the rows and special subsets of the columns are meaningful, others are not. A submatrix in A is said to be meaningful if and only if it is the cross product of a meaningful row subset and a meaningful column subset, in which case we call it an "allowed rectangle." The goal is to "explain" A as a sparse sum of weighted allowed rectangles. Specifically, we wish to find as few weighted allowed rectangles as possible such that, for all i,j, a_{ij} equals the sum of the weights of all rectangles which include cell (i,j).
In this paper we consider the natural cases in which the matrix dimensions are tree-ordered or linearly-ordered. In the tree-ordered case, we are given a rooted tree T1 whose leaves are the rows of A and another, T2, whose leaves are the columns. Nodes of the trees correspond in an obvious way to the sets of their leaf descendants. In the linearly-ordered case, a set of rows or columns is meaningful if and only if it is contiguous.
For tree-ordered data, we prove the explanation problem NP-Hard and give a randomized 2-approximation algorithm for it. For linearly-ordered data, we prove the explanation problem NP-Hard and give a 2.56-approximation algorithm. To our knowledge, these are the first results for the problem of sparsely and exactly representing matrices by weighted rectangles.

Asynchronous Code-Division Random Access Using Convex Optimization by Lorne Applebaum, Waheed U. Bajwa, Marco F. Duarte, Robert Calderbank. The abstract reads:
Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access channels for such applications. Traditional orthogonal signaling ignores the random nature of user activity in this problem and limits the total number of users to be on the order of the number of signal space dimensions. Contention-based schemes, on the other hand, suffer from delays caused by colliding transmissions and the hidden node problem. In contrast, this paper presents a novel asynchronous (non-orthogonal) code-division random access scheme along with a convex optimization-based MUD algorithm that overcomes the issues associated with orthogonal signaling and contention-based methods. Two key distinguishing features of the proposed algorithm are that it does not require knowledge of the delay or channel state information of every user and it has polynomial-time computational complexity. The main analytical contribution of this paper is the relationship between the performance of the proposed MUD algorithm and two simple metrics of the set of user codewords. The study of these metrics is then focused on two specific sets of codewords, random binary codewords and specially constructed algebraic codewords, for asynchronous random access. The ensuing analysis confirms that the proposed scheme together with either of these two codeword sets significantly outperforms the orthogonal signaling-based random access in terms of the total number of users in the system.
Following are three announcement for three talks, some have passed but what is important is the abstract of the talks:

iCME Colloquium, Resolution Analysis for Compressive Imaging
Information

* Wednesday
March 2, 2011
* 4:15 pm - 5:05 pm
* Bldg. 380, Rm. 380/380X

Albert Fannjiang (University of California, Davis)
In this talk we will focus on the issue of resolution when compressed sensing techniques are applied to imaging and inverse problems. The physical process of measurement consists of illumination/emission, wave propagation and reception/sampling, giving rise to measurement matrices more structured than those typically studied in the compressed sensing literature. We will show how to achieve the diffraction limit in diffraction tomography, inverse scattering and radio interferometry by using random sampling. We will also discuss the superresolution effect resulting from near-field measurements, random illumination and multiple measurements in conjunction with random sampling.
Fast dimensionality reduction: improved bounds and implications for compressed sensing
Event on 2011-01-20 16:10:00
Fast dimensionality reduction: improved bounds and implications for compressed sensing Colloquium | January 20 | 4:10-5 p.m. | 60 Evans Hall
Speaker: Rachel Ward, Courant Institute, New York University Sponsor: Mathematics, Department of
Embedding high-dimensional data sets into subspaces of much lower dimension is important for reducing storage cost and speeding up computation in several applications, including numerical linear algebra, manifold learning, and computer science. The relatively new field of compressed sensing is based on the observation that if the high-dimensional data are sparse in a known basis, they can be embedded into a lower-dimensional space in a manner that permits their efficient recovery through l1-minimization. We first give a brief overview of compressed sensing, and discuss how certain statistical procedures like cross validation can be naturally incorporated into this set-up. The latter part of the talk will focus on a near equivalence of two fundamental concepts in compressed sensing: the Restricted Isometry Property and the Johnson-Lindenstrauss Lemma; as a consequence of this result, we can improve on the best-known bounds for dimensionality reduction using structured, or fast linear embeddings. Finally, we discuss the Restricted Isometry Property for structured measurement matrices formed by subsampling orthonormal polynomial systems, and high-dimensional function approximation from a few samples.
Event Contact: 510-642-6550

at University of California, Berkeley
110 Sproul Hall
Berkeley, United States
Speaker: Qiyu Sun, Approximation Property in Compressive Sampling
Wednesday, January 19, 2011
2:00 PM to 4:00 PM
3076 Duncan Hall
Rice University
6100 Main St
Houston, Texas, USA

The null space property and the restricted isometry property for a measurement matrix are two basic properties in compressive sampling, and are closely related to the sparse approximation. In this talk, we introduce the sparse approximation property for a measurement matrix, a weaker version of the restricted isometry property and a stronger version of the null space property. We show that the sparse approximation property for a measurement matrix could be an appropriate condition to consider stable recovery of any compressible signal from its noisy measurements.

Finally, some summer jobs:

Internship Opportunity (2011 summer) at Mitsubishi Electric Research Labs (MERL), Cambridge, MA, USA (http://www.merl.com/)

Posting Date: Jan 23, 2011

Internship Positions: Multiple

MERL is the North American corporate research and development organization of the Mitsubishi Electric Corporation (MELCO). Based in Cambridge, MA, MERL offers a challenging and stimulating research environment and opportunity to pursue independent projects and receive authorship on publications. The imaging group at MERL does research concerning information capture/extraction/analysis and display including computer vision, computational photography, multi-projector systems, image processing, machine learning and 3D graphics & modeling.

MERL invites applications for summer internship in 2011 in the imaging group. Graduate students pursuing a Phd degree in EE, CS or a related discipline are encouraged to apply. Publications at the flagship conferences (ICCV/CVPR/SIGGRAPH) as a result of the internship are highly encouraged. Development will be a mix of prototyping in Matlab and/or C/C++ and strong programming skills are required.

Specific research topics of interest include sparse/dense 3D reconstruction, stereo and multi-view stereo, SLAM, structure light scanning, wide-angle imaging using catadioptric sensors and 1D signal processing on DSP's. Applicants are expected to be familiar with the fundamentals of computer vision and image/video processing, along with sufficient knowledge in these areas. Prior publication in these areas is a plus.