CS: Very High Speed Incoherent Projections for Superresolution, and a conference.

Stephane Mallat made a presentation at ETCV'08 (I mentioned it before). As some of you may know Stephane Mallat is known for his contribution to development of the wavelet framework.  He has also been involved in a start-up in the past few years. The start-up, initially called Let It Wave devised technologies around the bandelet families of functions (in particular in collaboration with Gabriel Peyre). It looks as though, the latest development of this start-up has been the conversion of today's videos into High Definition video. In that presentation entitled Sparse Geometric Superresolution, Stephane mentions that the challenge of up-conversion involves the ability to produce an increase of 20 times the number of initial information in the low resolution video.

As he explains, the chip that is supposed to produce this feat should cost $5 and it also has to use fast algorithms and matching pursuit don't do well in that very high speed conversion. The presentation in the video is very interesting in detailing the method. The thing I note is the thing he doesn't say in these exact words: In order to do a fast search in a dictionary, he projects the low resolution video onto an incoherent basis. From that projection, he uses a comparison between that projection and the projections of a very large dictionary unto that incoherent basis and does pattern matching.

A person has asked me before about doing CS with JPEGs: I guess one can do that for that purpose (superresolution). In a different area, we have seen this type of procedure being undertaken by Jort Gemmeke in speech problems ( Using sparse representations for missing data imputation in noise robust speech recognition by Jort Gemmeke and Bert Cranen ). At 7.5 Gbit/s, I wonder how we could use the LB-101M chip to do all kinds of superresolution beyond images....I think it also fits the description of hardware performing CS so I will include it in the CS hardware page. [ Update: I am told by Stephane Mallat that the LB-101M chip does not implement this algorithm. It implements a somewhat smarter algorithm given the hardware constraints]

I also found it funny that Stephane mentioned the testing procedure used by experts to gauge whether a new imaging technology is acceptable. They simply go into a room and watch images and movies for hours with the new technology and provide some feedback on a how good or bad it is.


That reminded of how Larry Hornbeck described to us how he had to make the DMD technology acceptable for imaging/projector technology. The technology is now integrated in DLP projectors but it took a while before the algorithm commanding (the DMD controller) the mirrors on the DMDs got a good feedback from the professionals. Larry had become an expert over time, and his team at Texas Instrument was constantly checking with him while they were improving the algorithm. At one point, the team seemed a little miffed that Larry would always find problems when they did not seem to exist. They then switched technologies in the projection room but Larry would still find the same problems. At which point, Larry and his team decided the DMD technology had indeed matured to the point that it would be hard for experts to find flaws. Larry received an Emmy awards in 1998 for the development of this technology. The DMD is also at the heart of the Rice single pixel camera.

Larry gave me one of his demonstration DMD at the end of his presentation! woohoo.  

On a totally unrelated note, a conference that features Compressed Sensing as a subject of interest is CHINACOM 2009: Int'l Conference on Communications and Networking in China,  Information and Coding Theory Symposium,  August 26-28, 2009, Xi'an, China.

CS: Freefalling, Hardware at 130,000 feet, Statistics on a cartoon, and a Silicon detector.

Here is a fantastic rendering of what it would look like to fall from Space (for those of you reading this through e-mail or an RSS feed, here is the direct link)



Credit: Kyle Botha.

This reminds me that you don't need a rocket to go up. Stratospheric balloons do that very well as can be seen from the view of a webcam that was on-board the HASP last year.

Credit: CosmoCam

For those of you interested in having some hardware at those altitudes, you may be interested in the new request for proposal by the HASP folks. The deadline is Dec. 19th.

The first cartoon video on CS has reached more than 1000 viewers (950 times being me hitting that replay button). The statistics provided by Youtube provide some insight about when the interest of the reader was the highest. I am not sure how they compute this but the first bump in this video is when CS is connected to underdetermined systems and linear algebra 101.

The video can be viewed here:

Finally, a video on a type of photon detector made out of Silicon that seems to have reached some breakthrough. More pixels, lower cost is our future, how can we integrate this in new types of CS cameras ?

CS: Greedy Signal Recovery Review, Motion Segmentation, Efficient Sampling and Stable Reconstruction,

I found three papers related to CS:

Greedy Signal Recovery Review by Deanna Needell, Joel Tropp and Roman Vershynin. The abstract reads:

The two major approaches to sparse recovery are L1-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. Even 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 logN), where N is the ambient dimension of the signal. This review summarizes these major advances.

ROMP and CoSaMP codes are accessible from the reconstruction section of the Big Picture. Let us also note the importance of the Restricted Isometry Constant. 

Moshe Mishali, Yonina Eldar and Joel Tropp just released Efficient Sampling and Stable Reconstruction of Wide Band Sparse Analog Signals ,  the asbtract reads:

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 ismuch 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.

The attendant talk is here. In a different direction, Shankar Rao, Roberto Tron, Rene Vidal, and  Yi Ma just released 

Motion Segmentation in the Presence of Outlying, Incomplete, and Corrupted Trajectories. The abstract reads: 

In this paper, we study the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence. Using the affine camera model, this problem can be cast as the problem of segmenting samples drawn from multiple linear subspaces. In practice, due to limitations of the tracker, occlusions, and the presence of nonrigid objects in the scene, the obtained motion trajectories may contain grossly mistracked features, missing entries, or corrupted entries. In this paper, we develop a robust subspace separation scheme that deals with these practical issues in a unified mathematical framework. Our methods draw strong connections between lossy compression, rank minimization, and sparse representation. We test our methods extensively on the Hopkins155 motion segmentation database and other motion sequences with outliers and missing data. We compare the performance of our methods to state-of-the-art motion segmentation methods based on expectation-maximization and spectral clustering. For data without outliers or missing information, the results of our methods are on par with the state-of-the-art results, and in many cases exceed them. In addition, our methods give surprisingly good performance in the presence of the three types of pathological trajectories mentioned above. All code and results are publicly available at http://perception.csl.uiuc.edu/coding/motion/.

Yi Ma and his team continue on doing wonders. Here they use the result in rank minimization and CS to provide robust trackers over missing data. 

And finally, here is a section of papers and presentations not strictly exactly focused on Compressed Sensing but rather that make use or reference Compressive as a neighboring technique. There the presentation entitled Pseudospectral Fourier reconstruction with IPRM by Karlheinz Gröchenig and Tomasz Hrycak.

Also, Arxiv now allows a full search in the text of the papers in its library. Here is a list of paper that mention Compressive Sensing without Compressive Sensing being the main subject of the paper:

• A proximal method for composite minimization, A.S. Lewis, S.J. Wright
• Comparing Measures of Sparsity, Niall P. Hurley, Scott T. Rickard
• Approximate Sparse Decomposition Based on Smoothed L0-Norm Hamed Firouzi, Masoud Farivar, Massoud Babaie-Zadeh, Christian Jutten
• Noise-Resilient Group Testing: Limitations and Constructions, Mahdi Cheraghchi
• Robust Regression and Lasso, Huan Xu, Constantine Caramanis, Shie Mannor
• Learning to rank with combinatorial Hodge theory, Xiaoye Jiang, Lek-Heng Lim, Yuan Yao, Yinyu Ye
  

CS: Compressed Sensing Phase Retrieval, Deterministic SFT, A generalization of Kolmogorov’s theory of n-widths for infinite dimensional spaces, a job.

From Wikimization, here is a newer version of Toward 0-norm Reconstruction, and a Nullspace Technique for Compressive Sampling as presented by Christine Law with Gary Glover at the Linear Algebra and Optimization Seminar (CME510), iCME, Stanford University, November 19, 2008.

Unlike what I said earlier, the paper entitled Compressed Sensing Phase Retrieval with Matthew Moravec, Justin Romberg and Richard Baraniuk can be found here.

Adi Akavia was speaking on Monday, December 8 2008 at MIT. The talk presentation reads:

Computing the Fourier transform is a basic building block used in numerous applications. For data intensive applications, even the O(N log N) running time of the Fast Fourier Transform (FFT) algorithm may be too slow, and sub-linear running time is necessary. Clearly, outputting the entire Fourier transform in sub-linear time is infeasible, nevertheless, in many applications it suffices to find only the \tau-significant Fourier transform coefficients, that is, the Fourier coefficients whose magnitude is at least \tau-fraction (say, 1%) of the energy (ie, the sum of squared Fourier coefficients). We call algorithms achieving the latter SFT algorithms. 

In this work we present a *deterministic* algorithm that finds the $\tau$-significant Fourier coefficients of functions f over *any finite abelian group G* in time polynomial in log|G|, 1/\tau and L_1(f) (for L_1(f) denoting the sum of absolute values of the Fourier coefficients of f). Our algorithm is robust to random noise. 

Our algorithm is the first deterministic and efficient (ie, polynomial in log|G|) SFT algorithm to handle functions over any finite abelian groups, as well as the first such algorithm to handle functions over Z_N that are neither compressible nor Fourier-sparse. Our analysis is the first to show robustness to noise in the context of deterministic SFT algorithms. Using our SFT algorithm we obtain (1) deterministic (universal and explicit) algorithms for sparse Fourier approximation, compressed sensing and sketching; (2) an algorithm solving the Hidden Number Problem with advice, with cryptographic bit security implications; and (3) an efficient decoding algorithm in the random noise model for polynomial rate variants of Homomorphism codes and any other concentrated and recoverable codes.

Hum.. (I put the emphasis in the text) here is another statement along the lines that sparsity is not being the main prerequisite condition for subsampling. I look forward to seeing more of that paper.

On December 17-19, 2008, at the Workshop on Optimization and Applications, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences in Sofia, Bulgaria, Ognyan Kounchev will give a talk entitled A generalization of Kolmogorov’s theory of n-widths for infinite dimensional spaces: applications to Compressive sensing. The abstract reads:

Recently, the theory of widths has got high interest due to its importance for the so-called Compressive sensing, see the works of D. Donoho, E. Candes, T. Tao, R. Baraniuk and others. On the other hand, the theory of n-widths of Kolmogorov (a kind of Optimal recovery theory) is not appropriate for the spaces of functions depending on several variables - this is seen from the simplest examples which one would like to have treated by a theory of Optimal recovery. We generalize the theory of n-widths of Kolmogorov by considering approximation by infinite-dimensional spaces of functions which have so far ”harmonic dimension n” in some sense. A large class of such spaces having ”harmonic dimension n” is provided by the solutions of elliptic differential operators of order 2n. We indicate possible applications to Compressive sensing.

Here is a new job posting for a post-doc in the group of Jean-Luc Starck at CEA near Paris. The description reads:

JOB OPPORTUNITY

Title of the job : Post-doctoral position (3 years), Signal/Image processing at CEA Saclay, Service d’Astrophysique. The Service d'Astrophysique (SAp) at CEA Saclay invites applications for a postdoctoral appointment in the area of data analysis/image processing of astronomical data to work with Jean-Luc Starck.

The CEA Saclay is a government research center situated 40 minutes from central Paris, France. The SAp has a wide interest in astrophysics ranging from planets to cosmology, with a specialisation in space missions (eg. Euclid, XMM-Newton, Herschel, PLANCK, JWST, Integral etc) and instrumentation (eg. Megacam on the Canada-France-Hawaii Telescope). The position is to work on sparse representation of astronomical data for different applications such as non-Gaussianity detection, inverse problem and compressed sensing.

Candidates should have a PhD in Image processing, Physics or Astronomy.

Previous experience in sparse representations (wavelet, curvelets, etc) and the development of data analysis methods is preferred, but experience in related areas is also suitable.

The position, funded for at least 3 years (up to 5 years), will be renewed on a yearly basis depending on scientific progress and achievement. The gross minimum salary will be 34,000€ annually (~2,260€ net per month), and will be adjusted according to experience and family situation. A minimum of 5,000 € per year of travel money for each position will also be provided, in addition to the usual funding support of any French institution (medical insurance, etc). Applicants are requested to send a CV, a list of publications, and a brief statement of research interests. This material together with three letters of reference should be sent by the closing date to

Jean-Luc Starck

Laboratoire Astrophysique des Interactions Multi-échelles

Irfu, Service d'Astrophysique, CEA Saclay,

F-91191 GIF-Sur-YVETTE CEDEX, France.

Email: check the flyer for more information.

The closing date for receipt of applications : February 28, 2009

The job posting has been to the CSJobs page.

The ICPR 2010 conference has Compressed Sensing as a subject of interest.

Image Credit: NASA/JPL/Space Science Institute, image of Tethys taken on December 9th, 2008.

CS: Compressive Sensing Technology Watch (Part Two)

Here is a presentation on the influence of GPUs in Compressive Sensing. It is located at: 

http://igorcarron.googlepages.com/cstechnologywatch

I also had to reframe the cultural references. Instead of Coluche a well known french artist, I replaced him with a more U.S centered cultural reference: Seinfeld's George Constanza. I explained previously why in CS: Coded Mask Imagers: What are they good for ? The George Costanza "Do the Opposite" Sampling Scheme. Here is the video.

CS: GPUCamp, Bring the Popcorn: ETVC'08 videos, Terry Tao's CS presentation and a new version of CVX

Let's bring out the popcorn, Frank Nielsen just let me know that the videos of the talks of ETVC'08 that occured two weeks ago are now available. As one can see (below) the lists features some of the people and techniques mentioned in this blog before. I particulary like the fact that some of these techniques are going to be increasinlgy important as folks are looking at performing tasks directly on the CS measurements as opposed to first performing reconstruction. 

The description of  the Emerging Trends in Visual Computing meeting is as follows:

This year, the international colloquium of LIX (Ecole Polytechnique) focuses on the emerging trends and challenges of the foundations of the cross-disciplinary area of visual computing. Visual computing encompasses computational geometry, computer graphics, machine vision and learning (just to name a few), and relies at its very heart on information geometry. Visual computing is underpinning major industrial applications as attested recently by the emerging fields of computational photography, 3D cinematography and advanced biomedical imaging.

The official website of the workshop is here. The videos of the talks are listed below:

• Opening of ETVC'08 by Jean-Marc Steyaert, Frank Nielsen
  
• Detection of Symmetries and Repeated Patterns in 3D Point Cloud Data by Leonidas Guiba
  
• Discrete Curvature Flow for Surfaces and 3-Manifolds by Xiaotian Yin
  
• Certified Mesh Generation by Jean-Daniel Boissonnat
  
• Information-Theoretic Algorithms for Diffusion Tensor Imaging by Baba C. Vemuri
  
• Statistical Computing on Manifolds for Computational Anatomy by Xavier Pennec
  
• Large-Scale Object Recognition Systems by Cordelia Schmid
  
• Recovering Shape and Motion from Video Sequences by Pascal Fua
  
• Computational Geometry from the Viewpoint of Affine Differential Geometry by Matsuzoe Hiroshi
  
• Unifying Subspace and Distance Metric Learning with Bhattacharyya Coefficient for Image Classification by Dimitris N. Metaxas
  
• Non-standard Geometries and Data Analysis by Suresh Venkatasubramanian
  
• Information Geometry and Its Applications by Shun-ichi Amari
  
• Information Geometry: Duality, Convexity and Divergences by Jun Zhang
  
• Computational Photography: Epsilon to Coded Imaging by Ramesh Raskar
  
• The Intrinsic Geometries of Learning by Richard Nock
  
• Applications of Information Geometry to Radar Signal Processing by Frédéric Barbaresco ( I have mentioned him before here)
  
• Constant-Working-Space Algorithms for Image Processing by Tetsuo Asano
  
• Sparse Geometric Super-Resolution by Stephane Mallat
  
• Sparse Sampling: Variations on a Theme by Shannon by Martin Vetterli
  
• Image Retrieval via Kullback Divergence of Patches of Wavelets Coefficients in the k-NN Framework by Michel Barlaud
  
• Machine learning and kernel methods for computer vision by Francis Bach
  
• 3D Visibility and Lines in Space by Sylvain Lazard
  
• Procedural Modeling of Architectures: Towards Large Scale Visual Reconstruction by Nikos Paragios
  
• 3D Video: A Fusion of Graphics and Vision by Markus Gross
  

Terry Tao is in Spain and posted his presentation on The uniform uncertainty principle and compressed sensing. 

Finally, Michael Grant and Stephen Boyd released Version 1.2 of CVX: Matlab Software for Disciplined Convex Programming.

CS: GPUCamp, 2 comments, large scale version of the SaMP package, CS with Sequential Observations, Instance Optimal Decoding by Thresholding in CS

Stefano Marchesini has just put up a presentation shown at the UTK Colloquium. This is a 39 MB movie of the slides. If y'all are not reading the comments, Stefano kindly mentioned the following aftter being featured here:

For fairness, the CS part was inspired by Matthew Moravec et al. "Compressive Phase Retrieval", Wavelets XII, SPIE 6701, No. 1. (2007)

It's funny, I did not see it listed on the Rice Repository. The closest I can find is this one.

Thong Do just released a large scale version of the Sparsity Adaptive Matching Pursuit package. More information can be found here. The link is also in the big picture reconstruction section.

Ramesh Raskar has updated his Camera Culture site. One can read more about his fascinating hardware development projects here. He is also recruiting.

Also found two new additions on the Rice Repository:

Compressed Sensing with Sequential Observations by Dmitry Malioutov, Sujay Sanghavi, Alan Willsky. The abstract reads:

Compressed sensing allows perfect recovery of a signal that is known to be sparse in some basis using only a small number of measurements. The results in the literature have focused on the asymptotics of how many samples are required and the probability of making an error for a fixed batch of samples. We investigate an alternative scenario where observations are available in sequence and can be stopped as soon as there is reasonable certainty of correct reconstruction. For the random Gaussian ensemble we show that a simple stopping rule gives the absolute minimum number of observations required for exact recovery, with probability one. However, for other ensembles like Bernoulli or Fourier, this is no longer true, and the rule is modified to trade off delay in stopping and probability of error. We also describe a stopping rule for the nearsparse case which tells when enough observations are made to reach a desired tolerance in reconstruction. Sequential approach to compressed sensing involves the solution of a sequence of linear programs, and we outline how this sequence can be solved efficiently.

and Instance Optimal Decoding by Thresholding in Compressed Sensing by Albert Cohen, Wolfgang Dahmen, and Ronald DeVore. The abstract reads:

Compressed Sensing seeks to capture a discrete signal x element of R^N with a small number n of linear measurements. The information captured about x from such measurements is given by the vector y = \phi x element of R^n where  is an n x N matrix. The best matrices, from the viewpoint of capturing sparse or compressible signals, are generated by random processes, e.g. their entries are given by i.i.d. Bernoulli or Gaussian random variables. The information y holds about x is extracted by a decoder
mapping R^n into R^N. Typical decoders are based on l1-minimization and greedy pursuit. The present paper studies the performance of decoders based on thresholding. For quite general random families of matrices , decoders
are constructed which are instance-optimal in probability by which we mean the following. If x is any vector in R^N, then with high probability applying \delta
to y = \phi x gives a vector x :=\Delta
(y) such that ||x-x^-|| less than  C_0 \sigma_k(x)_l2 for all k  less than a n / logN provided a is suciently small (depending on the probability of failure). Here \sigma_k(x)_l2 is the error that results when x is approximated by the k sparse vector which equals x in its k largest coordinates and is otherwise zero. It is also shown that results of this type continue to hold even if the measurement vector y is corrupted by additive noise: y = \phi x + e where e is some noise vector. In this case \sigma_k(x)_l2 is replaced by \sigma_k(x)_l2 + ||e||_l2 .

Finally, found on ArXiv,

L1Packv2: A Mathematica package for minimizing an $\ell_1$-penalized functional by Ignace Loris. The abstract reads:

L1Packv2 is a Mathematica package that contains a number of algorithms that can be used for the minimization of an $\ell_1$-penalized least squares functional. The algorithms can handle a mix of penalized and unpenalized variables. Several instructive examples are given. Also, an implementation that yields an exact output whenever exact data are given is provided.

The Mathematica package is here.

CS: Streaming Measurements in Compressive Sensing: l_1 Filtering, a DARPA SBIR announcement.

From the Rice repository site, there are a few papers I have not covered. Here is one: Streaming Measurements in Compressive Sensing: l_1 Filtering by M. Salman Asif and Justin Romberg. The abstract reads:

The central framework for signal recovery in compressive sensing is l_1 norm minimization. In recent years, tremendous progress has been made on algorithms, typically based on some kind of gradient descent or Newton iterations, for performing l_1 norm minimization. These algorithms, however, are for the most part “static”: they focus on finding the solution for a fixed set of measurements. In this paper, we will present a method for quickly updating the solution to some l_1 norm minimization problems as new measurements are added. The result is an “l_1 filter” and can be implemented using standard techniques from numerical linear algebra. Our proposed scheme is homotopy based where we add new measurements in the system and instead of solving updated problem directly, we solve a series of simple (easy to solve) intermediate problems which lead to the desired solution.

The attendant presentation is here. Of related intested is Salman Asif's thesis we mentioned earlier entitled: Primal Dual Pursuit: A homotopy based algorithm for the Dantzig selector. One can also read the presentation slides, errata listand attendant Matlab files.

For those of you who know what an SBIR is, here is a DARPA one (from here):

SB091-010           TITLE: Panoramic Helmet-Mounted Display and Processing

 

TECHNOLOGY AREAS: Sensors, Electronics

 

OBJECTIVE: Develop a prototype of a panoramic, wide field of view helmet-mounted display, which presents the user with information from a minimum 90 degree horizontal field of view (FOV) with a goal of 120 degree horizontal and 40 to 50 degree vertical field of view, including signal processing adaptable to scene content.   

 

DESCRIPTION: Significant advances have taken place in the development of large format imaging sensors, with mega-pixel sensors available in several spectral bands.  These large sensors, which cover a wide field of view, fulfill the requirements for many applications, but are especially important in helmet-mounted systems for both ground and pilotage applications.  However, the display technology essential to presenting the large amount of information generated by the sensor lags considerably behind the sensor technology.  Currently, display technology is limited in field of view, and does not have the integral signal processing to match the capability of large format sensors and to adapt the information to meet user needs. 

 

The need to efficiently display a large amount of information to the user is crucial to mission success.  Information must be available to detect threats at the periphery of vision, to discern details as needed by the situation, and to perform intricate tasks.  Meeting all of these requirements simultaneously requires a significant leap-forward in display and signal processing technology.  The display must meld the requirement for full panoramic field of view with the need for an adaptable, high resolution instantaneous field of view. 

 

The display must provide high image quality in a light weight package, with the ergonomics required for user acceptance, such as the center of mass optimized for head-mounted applications.  The display format must be extended beyond the current state of the art, leading to innovative concepts in Mega-pixel displays with a high visual acuity in the central region and lower resolution in the periphery of the display.  Novel signal processing and image reconstruction techniques must be applied to present the user with the essential scene content.  The goal is to develop innovative sampling techniques that require only a small percentage of the data to reconstruct high quality scene information.  These techniques have been demonstrated in radar and acoustic signal processing, but not implemented in helmet mounted displays.  Although signal processing techniques have been demonstrated, there is considerable risk in the implementation of these techniques in display systems.  However, the pay-off is large, enabling the user to grasp the large amount of information generated in a panoramic scene.     

 

Emerging technologies in compressive sampling, where the information rate may be much smaller than the bandwidth, enables the presentation of only the essential information without loss of scene content.  These new techniques can be integrated with wide field of view display components to present information from a wide field of view at minimum power, essential to helmet-mounted systems.  The integrated display/processor not only presents information to the user, but also integrates functions to reduce workload, increase the situational awareness and enhance the ability to perform essential tasks.

 

In military display applications, a wide field of view combined with the flexibility to perform multiple functions, and elimination of display artifacts that detract from image quality, are essential to user acceptance of the technology.  The display technology must have a fast response time so that the image is free of artifacts due to target movement or head-movement.  Frame update rate of at least 60 Hz minimizes image artifacts and blurring.  An innovative feature of the display technology should be the flexibility to integrate inputs from external sources as well as the ability to export selected areas to other sensor systems. 

 

The physical configuration of the display must conform to the user with an unobtrusive format, conformal with the helmet, fitting similar to a visor, and with the display configured with optimum binocular overlap to provide high resolution and a contiguous view of displayed information.  The brightness should be sufficient to present high contrast information, even in high light ambient environments.  Also, the physical configuration must be such that illumination from the display is visible only to the user and keeps the system convert.   

 

Applications include aviation and ground applications.  The signal processing functions should be adaptable, allowing the display processing system to be used in multiple environments.  

 

PHASE I: Define issues associated with the development of a novel concept in wide field of view display technology for helmet mounted applications; design the micro-system concept for panoramic helmet mounted display that includes adaptable compressive sampling to present essential scene content to the user.  Perform simulations to demonstrate significant features of the display and advantages in military ground and airborne applications.  Plans for Phase II will be proposed, including display component requirements and signal processing design. 

 

PHASE II: Demonstrate the wide field of view display concept demonstrator with panoramic field of view, showing central region visual acuity approaching 20/20, with a minimum of 8 bits per pixel with a goal of 16 bits per pixel; show viability of the signal processing approach, display component technology, and the integration of signal processing with the display.      

 

PHASE III: DUAL USE APPLICATIONS: Multiple applications for wide field of view display technology are in aircraft simulators and training systems.  The display will present information from a wide field of view and provide a realistic view of the scene, while the integral signal processing will maintain and enhance the details in the scene necessary to perform intricate tasks.        

 

REFERENCES:

1. Patterson R., Pierce B.J., Winterbottom M. C., “Perceptual Issues in the use of Head-Mounted Visual Displays” Journal of the Human Factors and Ergonomics Society, Vol 48 No. 3, 2006. pp 555-573.

 

2. Brickner M.S., “Helicopter Flights with Night-Vision Goggles-Human Factors Aspect” NASA Technical Memorandum 101039, March 1989.

 

3. E. J. Candès and M. Wakin. An introduction to compressive sampling. IEEE Signal Processing Magazine, March 2008 21-30. (pdf)

 

4. E. J. Candès. Compressive sampling. Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006. (pdf)

 

5. Compressive Optical MONTAGE Photography David J. Bradya, Michael Feldmanb, Nikos Pitsianisa, J. P. Guoa, Andrew Portnoya, Michael Fiddyc aFitzpatrick Center, Box 90291, Pratt School of Engineering, Duke University, Durham, NC 27708. 
Digital Optics Corporation, 9815 David Taylor Drive, Charlotte, NC 28262. 
Center for Optoelectronics and Optical Communications, University of North Carolina Charlotte, 9201 University City Blvd. Charlotte, NC 28223. 
Proc. of SPIE Vol. 5907 590708-7.

 

KEYWORDS: Helmet-mounted displays; wide field of view; visual perception.

 

TPOC:                    Dr. Stuart Horn

Phone:                   (571) 218-4271

Fax:                        (703) 741-0086

E-mail:                   Stuart.Horn@darpa.mil

 

Photo: Igor Carron, Greenland from 30000 feet.

CS: Block-Sparsity: Coherence and Efficient Recovery, some talks, Bayesian Optimization of MRI Sequences

Here is a new entry in arxiv entitled Block-Sparsity: Coherence and Efficient Recovery by Yonina Eldar and Helmut Bolcskei. The abstract reads:

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and we show that a block-version of the orthogonal matching pursuit algorithm recovers block k-sparse signals in no more than k steps if the block-coherence is sufficiently small. The same condition on block-sparsity is shown to guarantee successful recovery through a mixed l2/l1 optimization approach. The significance of the results lies in the fact that making explicit use of block-sparsity can yield better reconstruction properties than treating the signal as being sparse in the conventional sense thereby ignoring the additional structure in the problem.

I'll add the Block OMP (BOMP) algorithm to the Big Picture Reconstruction section. 

There is a seminar series at Vanderbilt on Compressed Sensing. I just noticed it but here are the last talks:

5. The Tiling Phenomenon of 1-bit Feedback Analog-to-Digital Converters

Truong-Thao Nguyen, City University of New York

Tuesday, December 2, 4:10-5:00, SC 1312

6. Compressive Signal Processing using Manifold Models

Mike Wakin, Colorado School of Mines

Tuesday, December 9, 4:10-5:00, SC 1312.

At Drexel, on January 12, 2009, Leo Grady will probably give a similar talk to the one we mentioned earlier. In the meantime,

Matthias Seeger has a new talk entitled Bayesian Optimization of MRI Sequences.

He mentions that "compared to earlier talks, this has a few more details about the inference

algorithm."

He still is looking for folks to work with him. It looks like most of the MRI trajectories in the Fourier space are in following a spiral and I wonder how the results of Meyer and Basarab would fit in this area of investigation ( I wondered this same point as while back). Maybe in the form of priors....

A Tutorial on Compressed Sensing (or Compressive Sampling or Linear Sketching) / Internships on the Riviera

Piotr Indyk just released his Tutorial on Compressed Sensing (or Compressive Sampling or Linear Sketching), given at the Workshop on Geometry and Algorithms last month.

His sparse recovery experiments wiki was mentioned earlier. Many items are of this presentation are detailed in Combining Geometry And Combinatorics: A Unified Approach to Sparse Signal Recovery by Radu Berinde, Anna Gilbert, Piotr Indyk, Howard Karloff and Martin Straus.

On a side note related to imaging: while taking a hit on the number of measurements (sketches) is not good (beause of the lower compression), there are instances where the physics makes it a difficult proposition to acquire a signal in some incoherent fashion. For background information on why, see the discussion with Ramesh Raskar (in CS: A Small Discussion with Ramesh Raskar and the Camera Culture Lab at MIT.) and with Greg Skinner (a specialist of Coded Aperture). In short, the SNR can go down real fast when a point like signal is too widespread on the detector, i.e. the Point Spread Function (PSF) is spread over too many pixels. This thought leads me to the question I have been pondering: can one map some of the current sparse measurement matrices (RIP-1) to an actual imaging Point Spread Function (PSF) that is not too wide on average.

While we are on the subject of Imaging, I have mentioned some internships offered by Thales on the subject of Compressed Sensing. The announcements are here and here. I talked to some of the folks at Thales and they tell me the internships are paid (900 euros but ask them from more accurate information) and are open to E.U. students as well if they apply early (need for clearance). Paid Internships on the French Riviera performing Compressed Sensing trade studies, I can think of worse student's jobs. I'll add the announcements on the CS Jobs page.