MCALab a toolbox for Signal and Image Decomposition and Inpainting, Some passing remark on inpainting and missing data.

A new version of the MCALab a toolbox for Signal and Image Decomposition and Inpainting by Jalal Fadili, Jean-Luc Starck, Michael Elad, David Donoho is now available here.

Presentation of the toolbox:

Morphological Component Analysis (MCA) of signals and images is an ambitious and important goal in signal processing; successful methods for MCA have many far-reaching applications in science and technology.

Because MCA is related to solving underdetermined systems of equations it might also be considered, by some, to be problematic or even intractable. Reproducible research is essential to give such a concept a firm scientific foundation and broad base of trusted results. MCALab has been developed to demonstrate key concepts of MCA and make them available to interested researchers and technologists. MCALab is a library of Matlab routines that implement the decomposition and inpainting algorithms that we previously proposed in our papers. The MCALab package provides the research community with open source tools for sparse decomposition and inpainting and is made available for anonymous download over the Internet. It contains a variety of scripts to reproduce the figures in our own articles, as well as other exploratory examples not included in the papers. One can also run the same experiments on one’s own data or tune the parameters by simply modifying the scripts. The MCALab is under continuing development by the authors; who welcome feedback and suggestions for further enhancements, and any contributions by interested researchers.

Requirements: Matlab 6.x and later and WaveLab802 or later. It has been successfully run with Matlab 6.x and 7.x under Unix Solaris/Linux/MacOSX. Can somebody please check it under Windows ?

The connection to Compressed Sensing (not that anything I am writing should be related to CS) is as follows: If one thinks of the mask as being part of a restriction operator on the measurement matrix as used in Compressed Sensing, then MCALab can be seen as a CS reconstruction solver for images. As mentioned earlier here in the context of images ( "When is missing data recoverable?" by Yin Zhang) and here in the context of voice recognition ( Using sparse representations for missing data imputation in noise robust speech recognition by Jort Gemmeke and Bert Cranen) it seems that projecting data that is irregularly sampled using random ensembles on top of a 0-1 mask enables one to produce convincing results. One can also note here a different measurement projection in the context of frequency inpainting ( SparSpec : a new method for fitting multiple sinusoids with irregularly sampled data, Sebastien Bourguignon, Hervé Carfantan and Torsten Böhm). In this last case, diracs and sine functions are maximally incoherent so there is no need for Gaussian ensembles.

Compressed Sensing: Additional Solvers, SpaRSA, ProxIT and an unnamed solver.

I am adding five new solvers to the Compressed Sensing Big Picture page.

* SpaRSA : It is described in Sparse Reconstruction by Separable Approximation by Mário Figueiredo, Robert D. Nowak and Stephen Wright. Mario tells me that it will be up for evaluation at some point in time.

* ProxIT: It was mentioned earlier in Compressed sensing in astronomy by Jerome Bobin, Jean-Luc Starck, and Roland Ottensamer.

* A solver based on IT-LARS and StOMP in Sparse Representation-based Image Deconvolution by Iterative Thresholding by Jalal Fadili and Jean-Luc Starck. The abstract reads:

Image deconvolution algorithms with overcomplete sparse representations and fast iterative thresholding methods are presented. The image to be recovered is assumed to be sparsely represented in a redundant dictionary of transforms. These transforms are chosen to offer a wider range of generating atoms; allowing more flexibility in image representation and adaptativity to its morphological content. The deconvolution inverse problem is formulated as the minimization of an energy functional with a sparsity-promoting regularization (e.g. ℓ1 norm of the image representation coefficients). As opposed to quadratic programming solvers based on the interior point method, here, recent advances in fast solution algorithms of such problems, i.e. Stagewise Iterative Thresholding, are exploited to solve the optimization problem and provide fast and good image recovery results. Some theoretical aspects as well as computational and practical issues are investigated. Illustrations are provided for potential applicability of the method to astronomical data.

* I also just saw a presentation detailing the underlying mechanics of another category of solvers called Monotone Operator Splitting. An example of which is Image Deconvolution under Poisson Noise using Sparse Representations and Proximal Thresholding Iteration by Francois-Xavier Dupe , Jalal Fadili and Jean-Luc Starck.

Let us note that in the first paper, there is a smart use of translation operators not unlike the restriction operators used in geophysics (as featured in Sparco).

* This last algorithm does not have name but is presented in Fast Sparse Representation using Smoothed L0 Norm by G. Hosein Mohimani, Massoud Babaie-Zadeh and Christian Jutten. The abstract reads:

In this paper we present an algorithm for complex-valued sparse representation. In our previous work we presented an algorithm for Sparse representation based on smoothed l_0 norm. Here we extend that algorithm to complex-valued signals. The proposed algorithm is compared to FOCUSS algorithm and it is experimentally shown that the proposed algorithm is about two or three orders of magnitude faster than FOCUSS while providing approximately the same accuracy.

Credit: NASA/JPL/Space Science Institute, Cassini on approach to Enceladus.

Compressed Sensing: A Faster Noiselet Transform and a Hybrid Reconstruction Algorithm

Laurent Jacques mentioned to me that he has built an even faster Noiselet transform than the one he sent me earlier, four times faster actually. This new version is located in the Codes section of his website. I am also pointing to that site from here.

I went to a presentation this afternoon by Sebastien Bourguignon (mentioned here before) in what amounts to inpainting in the frequency domain and discovered that he had already tried successfully something similar to the (now infamous :-) ) boosted algorithm suggested earlier. It is an hybrid algorithm that has a reweighted L1 algorithm as a second stage. It seems to me that with the large number of reconstruction methods, one could empirically build something that is very robust in the same way the Bellkor team did with the Netflix prize. During the Q/A, somebody suggested we look at SMLR, a greedy algorithm originally used in geophysics, I'll have to look into it.


Credit: NASA/JPL/University of Arizona, Proposed MSL Landing Site in Eberswalde Crater (PSP_007481_1560)

Compressed Sensing: Fast Noiselet Transform and Watching Stars.

[Update September 2010: Check Laurent Jacques' new entry on Noiselets with attendant (fast) code.]




The Noiselet Transform featured in the Monday Morning Algorithm 15 was not designed to be fast. However there is an increasing number of applications in the imaging world that requires it to be so. Laurent Jacques, another reader of this blog, decided to share his fast noiselet transform with us. In his words:

Since I needed that personally for my research, and since I read on Nuit Blanche that you were perhaps both interested in it for CS applications (or for Monday Morning Algos), I have "implemented" a Fast Noiselet Transform (1-D and 2-D). I put that in the attached archive FNT.zip (five .m files : fnt*d.m ifnt*.m, with *=1,2, + one internal file)

Actually, this is nothing but a slight variation of a Fast Hadamard Transform found on Matlab exchange, but it does the job. The initial Hadamard code is the one of Gylson Thomas at the Mathworks site: fwht1d.zip and fwht2d.zip

I liked Laurent's implementation (seen on both of your blogs) but, if I'm right, it was just for the noiselet matrix construction and not for a fast noiselet transform. This matrix is however very helpful for small-length vector multiplications. I have checked that a multiplication with Psi'=Build_Noiselets' and the use of fnt1d() provides the same outputs.

The implementation of this fast algorithm requires N log2 N additions and subtractions, with N being the total number of elements in the signals. It is now listed in the Compressed Sensing Code page and can be downloaded here. It's a coincidence but I just attended a talk by Jean-Luc Starck where he described the scheme to be used on Herschel in 2009, which will use a 2-D randomized noiselet transform.

Thank you Laurent.

The disclaimer for using this script is listed here.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.

CoSaMP, CVX , Mapping and Search and Rescue.

I have reshaped David Mary's script presented in MMA14 for CoSaMP and put it in the Compressive Sensing Code section. If there is any mistake, it's mine.


CVX: Matlab Software for Disciplined Convex Programming by Michael Grant, Stephen Boyd, and Yinyu Ye seems to have a larger Users' Guide.

I have found this interesting kit that may provide much ability in terms on performing some type of compressive sensing with cameras. Please note the heart shape coming from out of focus light in the photo above. More information can be found here or on lensbabies site. Instead of cutting off a lens housing, one can directly buy one to do some heterodyning camera. But I am sure we can think of even better things.




While some people seem to think that you need a GPS-Camera phone to know where you are (the eye-phone) other people like James Hays and Alexei Efros seem to trust the crowd to do part of the job as mentioned in im2gps: estimating geographic information from a single image.


It now looks like we can use satellite imagery to find the boats that slowed down the internet. This needs to be implemented in search and rescue operations. The search for Jim Gray showed that the use of this type of imagery took too long to be processed to be useful for search and rescue teams. On May 31, 2008, there will be a tribute to Jim Gray at Berkeley, I don't think I will be able to attend. I still believe that the main challenges listed here are not solved. I have mentioned some solutions (1, 2) by I am sure more can be found. All the entries on search and rescue operations can be found here. Following up on that, Alexandre Jenny tells me they have started to implement the orthographic projection capability in Autopano. This is a very good news as it will provide the ability to do low level flying, collect images and make maps out of them. This would be a very important capability in case of major disaster ("but that can’t be — it’s still in Google Maps!": Making maps using commercial overflights ). I definitely need to put together a page that summarize all the entries written in this blog on the subject since it seems to be of interest to different sets of people (search and rescue teams, journalists,...)

Monday Morning Algorithm 15: Building a Noiselet Basis and Measurement Matrix

For today's algorithm, Laurent Duval, a reader of this blog, decided to implement the noiselet basis of Coifman, Geshwind and Meyer [1] and share it. This basis has the particularity of being incoherent with the Haar Basis and therefore it is of particular interest in imaging in the compressed sensing framework (since pixels are Heaviside/Haar functions). It was mentioned before here and here. The script is available here but is also part of the Monday Morning Algorithm page and the Compressed Sensing code page as well.

function [noiselet_Matrix] = Build_Noiselets(n_Power)

% [noiselet_Matrix] = Build_Noiselets(n_Power)
% Built an orthonormal noiselet matrix with 2^n_Power
% In: n_Power (integer); default: n_Power = 5 (n_Sample = 2^n_Power = 32)
% Out: noiselet_Matrix (complex array); default (no outpu): display real and
% imaginery parts
% Example: noiselet_Matrix_1024 = Build_Noiselets(10);
%
% Comments: no optimization at all, suggestions welcome
% Creation: 2008/04/10
% Update: 2008/04/13
%
% Author: Laurent Duval
% URL: http://www.laurent-duval.eu

if nargin == 0
n_Power = 5;
end
n_Sample = 2^n_Power;

noiselet_Matrix = zeros(n_Sample,2*n_Sample-1);
noiselet_Matrix(:,1) = 1;
coef1 = 1 - i;
coef2 = 1 + i;
vect_Fill = zeros(n_Sample/2,1);
for i_Col = 1:n_Sample-1
vect_2x = [noiselet_Matrix(1:2:n_Sample,i_Col);vect_Fill];
vect_2x_1 = [vect_Fill;noiselet_Matrix(1:2:n_Sample,i_Col)];
noiselet_Matrix(:,2*i_Col) = coef1*vect_2x + coef2*vect_2x_1;
noiselet_Matrix(:,2*i_Col+1) = coef2*vect_2x + coef1*vect_2x_1;
end
noiselet_Matrix = 1/n_Sample*noiselet_Matrix(:,n_Sample:2*n_Sample-1);

if nargout == 0
figure(1)
subplot(1,2,1)
imagesc(real(noiselet_Matrix))
xlabel('Real part')
subplot(1,2,2)
imagesc(imag(noiselet_Matrix))
xlabel('Imaginery part')
end

Laurent is making some anagram on noiselets in his blog. As usual now, the disclaimer for using this script is listed here.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.

Reference: [1] R. Coifman, F. Geshwind, and Y. Meyer. Noiselets. Appl. Comp. Harmonic Analysis, 10:27–44, 2001.

Compressed Sensing: Bayesian Experimental Design for Compressed Sensing, CS Kalman Filter, Sparse Approximate Solution of PDE and more.

After the landmark paper of Roummel Marcia and Rebecca Willett here is a new batch of similarly interesting papers. Laurent Duval forwarded me this paper entitled Bayesian Experimental Design for Compressed Sensing by Hannes Nickisch and Matthias Seeger. The abstract reads:

Compressed sensing (CS) can be addressed as instance of Bayesian experimental design, which is based on similar models than common estimation (or energy minimisation) methods, but fundamentally differs from the latter, in that estimates of uncertainty and correlations of latent variables are maintained. The Bayesian computations are approximated by the expectation propagation fixed point algorithm, which is scaled up to the application of interest here through a novel scheduling mechanism, exploiting the fact that marginal uncertainty estimates are available at all times. An important application of CS is the optimisation of architectures for measuring natural images. In a large study, we compare various CS reconstruction methods utilising random measurement filters from different ensembles to a number of techniques which sequentially search for these filters, including our own, and Bayesian projection optimisation [1]. We find that a simple heuristic of measuring wavelet coefficients in a fixed, top-down ordering significantly outperforms CS methods using random measurements; the approach of [1] performs even worse. In contrast, our Bayesian design method learns filters that outperform the wavelet heuristic. Our results show that the property of incoherence of a measurement design, which plays a central role in the “unstructured except for random sparsity” theoretical CS setting, bears no significance for measuring real natural images. Our framework is not restricted to sparse signals, other notions of signal or noise structure can easily be accommodated. We give concrete ideas how our method can be scaled up to large signal representations.

Also found on arxiv.org:

If one were to consider signals living on a manifold, one could think of a way to follow the evolution of that signal using Particle Filtering on Riemannian Manifolds. Before we get to that stage, Namrata Vaswani looks at Kalman Filtered Compressed Sensing. The abstract reads:

We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear “incoherent” measurements, in real-time (causally). The signals are sparse in some transform domain referred to as the sparsity basis. For a single spatial signal, the solution is provided by Compressed Sensing (CS). The question that we address is, for a sequence of sparse signals, can we do better than CS, if (a) the sparsity pattern of the signal’s transform coefficients’ vector changes slowly over time, and (b) a simple prior model on the temporal dynamics of its current non-zero elements is available. The overall idea of our solution is to use CS to estimate the support set of the initial signal’s transform vector. At future times, run a reduced order Kalman filter with the currently estimated support and estimate new additions to the support set by applying CS to the Kalman innovations or filtering error (whenever it is “large”).

It was just a question of time, I talked before about solving an integral equation using CS, but one should first consider solving PDEs. Sadegh Jokar, Volker Mehrmann, Marc Pfetsch and Harry Yserentant do just that in Sparse Approximate Solution of Partial Differential Equations. The abstract reads:

A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure is presented that uses linear programming to find a good approximation to the sparse solution on a given refinement level. Then only those parts of the mesh are refined that belong to nonzero expansion coefficients. Error estimates for this procedure are refined and the behavior of the procedure is demonstrated via some simple elliptic
model problems.

one notes the appearance of the tree structure. Some of the authors ( Sadegh Jokar and Marc Pfetsch) have also written Exact and Approximate Sparse Solutions of Underdetermined Linear Equations. The abstract reads:

In this paper, we empirically investigate the NP-hard problem of finding sparsest solutions to linear equation systems, i.e., solutions with as few nonzeros as possible. This problem has received considerable interest in the sparse approximation and signal processing literature, recently. We use a branch-and-cut approach via the maximum feasible subsystem problem to compute optimal solutions for small instances and investigate the uniqueness of the optimal solutions. We furthermore discuss five (modifications of) heuristics for this problem that appear in different parts of the literature. For small instances, the exact optimal solutions allow us to evaluate the quality of the heuristics, while for larger instances we compare their relative performance. One outcome is that the so-called basis pursuit heuristic performs worse, compared to the other methods. Among the best heuristics are a method due to Mangasarian and a bilinear approach.

This was a preprint before but this is the final version: Computation and Relaxation of Conditions for Equivalence between l1 and l0 Minimization by Yoav Sharon, John Wright and Yi Ma. The abstract reads:

In this paper, we investigate the exact conditions under which the l1 and l0 minimizations arising in the context of sparse error correction or sparse signal reconstruction are equivalent. We present a much simplified condition for verifying equivalence, which leads to a provably correct algorithm that computes the exact sparsity of the error or the signal needed to ensure equivalence. Our algorithm is combinatorial in nature, but for moderate-sized matrices it produces the exact result in a reasonably short time. For l1-l0 equivalence problems involving tall encoding matrices (highly robust error correction) and or wide overcomplete dictionaries (sparse signal reconstruction from few measurements), our algorithm is exponentially faster than the only other algorithm known for this problem. We present an example application that requires such matrices, for which our algorithm can greatly assist with real system design. We also show how, if the encoding matrix is imbalanced, an optimal diagonal rescaling matrix can be computed by linear programming, so that the rescaled system enjoys the widest possible equivalence.

Credit: NASA/JPL/University of Arizona, Phobos, a Moon of Mars as photographed by HiRISE on March 23, 2008.

Compressed Sensing: Compressive Coded Aperture Superresolution Image Reconstruction, TOMBO, CASSI

It's Friday and you thought that you'd go home tonight being bored and all. Too bad, you started reading this entry. The good stuff just came out from the DISP group at Duke and other researchers working with them.

First and foremost, Roummel Marcia and Rebecca Willett introduce us to Compressive Coded Aperture Superresolution Image Reconstruction. It was presented at ICASSP last week. The abstract reads:

Recent work in the emerging field of compressive sensing indicates that, when feasible, judicious selection of the type of distortion induced by measurement systems may dramatically improve our ability to perform reconstruction. The basic idea of this theory is that when the signal of interest is very sparse (i.e., zero-valued at most locations) or compressible, relatively few incoherent observations are necessary to reconstruct the most significant non-zero signal components. However, applying this theory to practical imaging systems is challenging in the face of several measurement system constraints. This paper describes the design of coded aperture masks for superresolution image reconstruction from a single, low-resolution, noisy observation image. Based upon recent theoretical work on Toeplitz structured matrices for compressive sensing, the proposed masks are fast and memory-efficient to compute. Simulations demonstrate the effectiveness of these masks in several different settings.

There is a good explanation of Coded Aperture Imaging (a subject covered before here, here and here), they then make a very illuminating statement on MURAs and then continue with how compressed sensing is literally changing the hardware (in particular masks) but notice:

However, there currently exist few guiding principles for designing coded aperture masks for nonlinear reconstruction methods.

and then they get on to

extend these results [on Toeplitz matrices mentioned here] to pseudo-circulant matrices and use them to motivate our mask design.

The conclusion state:

This paper has demonstrated that coded apertures designed to meet the Restricted Isometry Property [7] can improve our ability to perform superresolution image reconstruction from noisy, low resolution observations. In particular, building from the theory of RIPs for Toeplitz-structured matrices for compressive sensing [10], we establish a method for generating coded aperture masks in both the conventional coded aperture setting and a Fourier imaging setting; these random masks can be shown to result in an observation matrix which, with high probability, satisfies the RIP. Furthermore, simulations demonstrate that these masks combined with l2 - l1 minimization reconstruction methods yield superresolution reconstructions with crisper edges and improved feature resolution over reconstructions
achieve without the benefit of coded apertures.

A very good paper to ponder over the week-end.

Mohan Shankar, Rebecca Willett, Nikos Pitsianis, Timothy Schulz, Robert Gibbons, Robert Te Kolste, J. Carriere, C. Chen, D. Prather, David Brady write about TOMBO: Thin infrared imaging systems through multi-channel sampling.

The abstract reads:

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3mmand achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.

We talked about this article of Ashwin Wagadarikar, Renu John, Rebecca Willett, and David Brady before but I never put the abstract on. Here it is: Single disperser design for coded aperture snapshot spectral imaging,

We present a single disperser spectral imager that exploits recent theoretical work in the area of compressed sensing to achieve snapshot spectral imaging. An experimental prototype is used to capture the spatiospectral information of a scene that consists of two balls illuminated by different light sources. An iterative algorithm is used to reconstruct the data cube. The average spectral resolution is 3.6 nm per spectral channel. The accuracy of the instrument is demonstrated by comparison of the spectra acquired with the proposed system with the spectra acquired by a nonimaging reference spectrometer.

And now, I am impatiently waiting for these two papers:

• Compressive coded aperture video reconstruction, Roummel F. Marcia and Rebecca M. Willett, Submitted to 2008 European Signal Processing Conference (EUSIPCO).
• Fast disambiguation of superimposed images for increased field of view, Roummel F. Marcia, Changsoon Kim, Jungsang Kim, David Brady, and Rebecca M. Willett, Submitted to 2008 IEEE International Conference on Image Processing (ICIP).

Compressed Sensing: CS measurements of a field of Diracs, Partial Fourier vs Gaussian Ensembles

Yesterday, we looked at the reconstruction issue arising when one compares the true solution to the one found through different algorithms. We found that when a high accuracy was needed, one could not rely on the current crop of reweighted algorithms. These algorithms do find a solution with fewer terms but the accuracy of these terms is not optimal compared to the greedy algorithms. Blue Pill / Red Pill: Pick you poison.
Today, we are running the second version of MMA14 and show that for an image that is sparse in the space domain (see above), the Random Partial Fourier Transform


does a better job than a Gaussian ensemble.

(all these plots were produced with tol1 =1 e-3).

This is not unexpected. Without any computation of incoherence, it seems obvious that a Dirac (our image here is composed of several diracs) would be more incoherent with regard to a Fourier function than a function that mimic several diracs (Gaussian ensemble). Let us recall in this example that the image is an 8 by 8 image, i.e. with a least square method (L2 based reconstruction), we would need 64 measurements. The sparsity of the image is 5. In other words, if I had a normal detector taking measurements and sending it through the pipeline, I would naively need to transfer 5 information about the peaks height and 10 information about their location (x,y for each peak) or a total of 15 information. If I were to use a CS detector, 15 information (measurements) would yield above 90 percent chance of recovering the signal whereas 17 CS measurements would yield a 100 percent recovery.

This is an ideal case for one reason. When receiving the signal, one doesn't know the true signal. I would not be surprised if we could use the solution with n measurements and the solution with n+1 measurements and obtain "faster" convergence.

Compressed Sensing: a blog, Autonomous geometric precision error estimation in low-level computer vision tasks, Neuroscience Datasets

Image via Wikipedia

I just recently found a blog that seems to focus on Compressed Sensing. In all, I have to say that Google is not doing a great job at taking into account labels from its own platform. In particular, I have found some odd discrepancies between the pagerank of some pages and the number of people that use Google reader to view them. Anyway, the blog of Andrés Corrada-Emmanuel entitled De Rerum Natura brings up some interesting applications in the determination of elevation models (DEM) from photographs as he has to deal with underdetermined systems of equations.. The postings are at:

http://www.corrada.com/blog/category/compressed-sensing/

he just had his paper accepted at ICML 08. The title is Autonomous geometric precision error estimation in low-level computer vision tasks by Andrés Corrada-Emmanuel and Howard Schultz. The abstract reads:

Errors in map-making tasks using computer vision are sparse. We demonstrate this by considering the construction of digital elevation models that employ stereo matching algorithms to triangulate real-world points. This sparsity, coupled with a geometric theory of errors recently developed by the authors, allows for autonomous agents to calculate their own precision independently of ground truth. We connect these developments with recent advances in the mathematics of sparse signal reconstruction or compressed sensing. The theory presented here extends the autonomy of 3-D model reconstructions discovered in the 1990s to their errors.

This is new. I don't think I have ever seen anybody talking about precision errors being a sparse signals before.


With the Netflix competition, we saw a lot of very interesting developments. One of them, as Andrew Gelman points out, is the fact that with a flurry of algorithms to choose from, data is paramount in leading to new and improved findings. An example of something similar in Neuroscience is the neuron challenge mentioned before. However, as echoed in this entry by Hal Daume III ( Those Darn Biologists...) there is very little incentive for biologists to publish their results with an analysis using new algorithms: This is not getting their papers published. A new initiative may help in that respect: the CRCNS - Collaborative Research in Computational Neuroscience - Data sharing activity is making biological / neuroscience datasets available for download here. This is prodigious idea. It currently lists datasets in:

• Primary visual cortex
• Auditory cortex
• Avian Auditory
• Hippocampus
• Eye movements

While The following additional data sets will be available by about June 2008:

• V4 responses to synthetic parametric stimuli. (From Jack Gallant lab, UC Berkeley).
• Responses in areas V1, V2 and V4 using precisely the same stimuli. Data collected to facilitate functional comparisons across successive stages of sensory processing. (From Jack Gallant lab, UC Berkeley).
• Tutorial on understanding intracellular recordings in sensory areas and accompanying data. The data are intracellular (whole-cell patch) recordings obtained in vivo from visual, auditory, somatosensory, and motor areas of the neocortex by the laboratories of Judith Hirsch, USC; Anthony Zador, CSHL; Michael DeWeese, UC Berkeley and Michael Brecht, Humboldt University Berlin. These data include not only spikes but also membrane voltages or currents generated by synaptic connections and intrinsic membrane channels.
• Synaptic plasticity data – Cortical slice data acquired in order to examine the effects of complex spike trains in the induction of long-term synaptic modification and recordings of primary visual cortical neurons made during stimulation. (From Yang Dan lab, UC Berkeley).
• Recordings from hippocampal CA1 neurons during open field foraging. (From Buzsáki lab, Rutgers University).