CS: CS for radio interferometry, Compressive Holography, SPIR-iT, CS in Multi-hop Sensor Networks, Split Bregman Iteration for CS

Today, there are several papers I found thanks to different blogs. This is great.

Compressed sensing for radio interferometry: spread spectrum imaging techniques by Yves Wiaux, Gilles Puy, Yannick Boursier and Pierre Vandergheynst. The abstract reads:

We consider the problem of reconstruction of astrophysical signals probed by radio interferometers with baselines bearing a non-negligible component in the pointing direction. The visibilities measured essentially identify with a noisy and incomplete Fourier coverage of the product of the planar signals with a linear chirp modulation. We analyze the related spread spectrum phenomenon and suggest its universality relative to the sparsity dictionary, in terms of the achievable quality of reconstruction through the Basis Pursuit problem. The present manuscript represents a summary of recent work.

Compressive Holography by David Brady, Kerkil Choi, Daniel L. Marks, Ryoichi Horisaki and Sehoon Lim. The abstract reads:

Compressive sampling enables signal reconstruction using less than one measurement per reconstructed signal value. Compressive measurement is particularly useful in generating multidimensional images from lower dimensional data. We demonstrate single frame 3D tomography from 2D holographic data.

David mentions this publication and another one on his blog (Multiscale lens design and compressive holography). Andrew Portnoy one of David's students has just released his Ph.D thesis entitled: Coded Measurement For Imaging and Spectroscopy. The abstract reads:

This thesis describes three computational optical systems and their underlying coding strategies. These codes are useful in a variety of optical imaging and spectroscopic applications. Two multichannel cameras are described. They both use a lenslet array to generate multiple copies of a scene on the detector. Digital processing combines the measured data into a single image. The visible system uses focal plane coding, and the long wave infrared (LWIR) system uses shift coding. With proper calibration, the multichannel interpolation results recover contrast for targets at frequencies beyond the aliasing limit of the individual subimages. This theses also describes a LWIR imaging system that simultaneously measures four wavelength channels each with narrow bandwidth. In this system, lenses, aperture masks, and dispersive optics implement a spatially varying spectral code.

David also has another thought provoking blog entry entitled: The coming data storm

In a different direction, we have SPIR-iT: Iterative Self Consistent Parallel Imaging Reconstruction from Arbitrary k-Space by Michael Lustig and John Pauly. The abstract reads:

A new approach to autocalibrating, coil-by-coil parallel imaging reconstruction is presented. It is a generalized reconstruction framework based on self consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k-space sampling patterns. The formulation can flexibly incorporate additional image priors such as off resonance correction and regularization terms. Several iterative strategies to solve the posed reconstruction problem in both image and k-space domain are presented. These are based on projection over convex sets (POCS) and conjugate gradient (CG) algorithms. Phantom and in-vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off-resonance correction and non-linear regularization are also demonstrated.

Spatially-Localized Compressed Sensing and Routing in Multi-hop Sensor Networks by Sungwon Lee, Sundeep Pattem, Maheswaran Sathiamoorthy, Bhaskar Krishnamachari, and Antonio Ortega. The abstract reads:

We propose energy-efficient compressed sensing for wireless sensor networks using spatially-localized sparse projections. To keep the transmission cost for each measurement low, we obtain measurements from clusters of adjacent sensors. With localized projection, we show that joint reconstruction provides significantly better reconstruction than independent reconstruction. We also propose a metric of energy overlap between clusters and basis functions that allows us to characterize the gains of joint reconstruction for different basis functions. Compared with state of the art compressed sensing techniques for sensor network, our simulation results demonstrate significant gains in reconstruction accuracy and transmission cost.

Following up Lianlin Li's blog on Compressive Sensing there is:

Curvelet-Wavelet Regularized Split Bregman Iteration for Compressed Sensing by Gerlind Plonka and Jianwei Ma. The abstract reads:

Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows to recover this signal from much fewer samples than the Shannon-Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. But such frames can sparsely represent special structures in images differently well. For a suitable recovery of images, we propose new models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = Φu + \epsilon with the measurement matrix Φ element of RK×N, K \lt N, we consider a constrained optimization problem of the form argmin u,ϑc,ϑw {Λcϑc1 + Λwϑw1 + 1 2f − Φu22} such that ϑc = Ψcu, ϑw = Ψwu (“denoising model”). Here Ψc and Ψw are the transform matrices corresponding to the two frames, and the diagonal matrices Λc, Λw contain the weights for the frame coefficients. Alternatively, if K  N, and if the noise
is negligibly small, we consider the “reconstruction model” argmin u,ϑc,ϑw {Λcϑc1 + Λwϑw1} such that there exists a vector u e;ement of RN with f = Φu, ϑc = Ψcu, and ϑw = Ψwu. We present efficient iteration methods to solve these optimization problems, based on Alternating Split Bregman algorithms. The convergence of these iteration schemes will be proved by showing that they can be understood as special cases of the Douglas-Rachford Split algorithm. Numerical experiments for compressed sensing based Fourier domain random imaging show good performances of the proposed curvelet-wavelet regularized split Bregman (CWSpB) methods, where we particularly use a combination of wavelet and curvelet coefficients as sparsity constraints.

Finally, Marco Duarte just got an IPAM Postdoc. Good luck Marco !


Credit: NASA via the Bad Astronomy blog. The tapes of the Apollo 11 landing that occured 40 years ago.