Mike Davies just let me know of a job announcement for a research Fellow at the University of Edinburgh,UK for three years starting March 1, 2009. I am adding it to Compressive Sensing jobs section. Looks like The Google has not indexed it yet, woohoo ... we are going faster than The Google.The sampling approach of the first paper/poster strangely ressembles the result by Yves Meyer, Basarab Matei featured in A variant on the compressed sensing of Emmanuel Candes (I talked about it here, here and here in reference to MRI). The paper is entitled: Highly Undersampled 3D Golden Ratio Radial Imaging with Iterative Reconstruction by Mariya Doneva, Holger Eggers , J. Rahmer , Peter Börnert and Alfred Mertins. The introduction reads:
Compressed Sensing (CS) [1,2] suggests that using nonlinear reconstruction algorithms based on convex optimization an accurate signal reconstruction can be obtained from a number of samples much lower than required by the Nyquist limit. Recently, CS was demonstrated for MR imaging from undersampled data [3, 4]. Prerequisites for a good image reconstruction are the image compressibility and the incoherence of the sampling scheme. To exploit the full potential of CS, measurement samples should be acquired at random. However, random sampling of the k-space is generally impractical. Variable density sampling schemes (radial, spiral) lead to incoherent aliasing and are also advantageous because of their higher sampling density about the k-space origin, where most of the signal energy is contained. 3D variable density sampling is potentially appropriate for CS, because the noise-like aliasing is distributed within the complete volume, allowing high undersampling factors. Image reconstruction from a low number of measurements could be very useful for dynamic 3D imaging, to reduce the often long acquisition times and thus improve temporal resolution in 3D MRI. In this work, we demonstrate the applicability of CS for 3D dynamic imaging using highly undersampled 3D radial acquisition with golden ratio profile ordering [5,6].
and from the same group of folks we also have: Model-based Compressed Sensing reconstruction for MR parameter mapping by Mariya Doneva, Christian Stehning, Peter Börnert, Holger Eggers and Alfred Mertins. The introduction reads:
Compressed Sensing [1-4] suggests that compressible signals can be reconstructed from far less samples than required by the Nyquist-Shannon sampling theorem. Signal recovery is achieved by Basis Pursuit (BP) [2] or greedy algorithms like Orthogonal Matching Pursuit (OMP) [4]. The latter has weaker performance guarantees, but it is often faster and is thus an attractive alternative to BP. Most commonly, orthonormal bases are applied as a sparsifyingtransform. However, allowing the signal to be sparse with respect to an overcomplete dictionary adds a lot of flexibility with regard to the choice of the transform and could improve the transform sparsity. MR parameter mapping measurements of relaxation times T1 and T2, diffusion coefficients, etc. require the acquisition of multiple images of the same anatomy at varying parameters, which is associated with long acquisition times. These data are described by a model with only few parameters, which could be used to design a model-based overcomplete dictionary for CS reconstruction. In this work we demonstrate this approach for the acceleration of T1 mapping data acquisition.
I also found: Rate Distortion Behavior of Sparse Sources by Claudio Weidmann, Martin Vetterli. The abstract reads:
The rate distortion behavior of sparse memoryless sources is studied. Such sources serve as models for sparse representations and can be used for the performance analysis of "sparsifying" transforms like the wavelet transform, as well as nonlinear approximation schemes. Under the Hamming distortion criterion, R(D) is shown to be almost linear for sources emitting sparse binary vectors. For continuous random variables, the geometric mean is proposed as a sparsity measure and shown to lead to upper and lower bounds on the entropy, thereby characterizing asymptotic R(D) behavior. Three models are analyzed more closely under the mean squared error distortion measure: continuous spikes in random discrete locations, power laws matching the approximately scale-invariant decay of wavelet coefficients, and Gaussian mixtures. The latter are versatile models for sparse data, which in particular allow to bound the suitably defined coding gain of a scalar mixture compared to that of a corresponding unmixed transform coding system. Such a comparison is interesting for transforms with known coefficient decay, but unknown coefficient ordering, e.g. when the positions of highest-variance coefficients are unknown. The use of these models and results in distributed coding and compressed sensing scenarios is also discussed.
Finally, Matching Pursuit Shrinkage in Hilbert Spaces by Tieyong Zeng, and Francois Malgouyes. The abstract reads:
This paper contains the research on a hybrid algorithm combining the Matching Pursuit (MP) and the wavelet shrinkage. In this algorithm, we propose to shrink the scalar product of the element which best correlates with the residue before modifying. The study concerns a broad family of shrinkage functions. Using weak properties of these shrinkage functions, we show that the algorithm converges towards the orthogonal projection of the data on the linear space generated by the dictionary, modulo a precision characterized by the shrinkage function. In the deterministic settings, under a mild assumption on the shrinkage function (for instance, the hard shrinkage satisfies this assumption), this algorithm converges in a finite time which can be estimated from the properties of the shrinkage function. Experimental results show that in the presence of noise, the new algorithm does not only outperform the regular MP, but also behaves better than some other classical Greedy methods and Basis Pursuit Denoising model when used for detection.
Image Credit: NASA/JPL/Space Science Institute. Dione as seen by Cassini last friday.
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