CS: Acoustic Kaleidoscope, reducing interference in EEG and visual resolution and cone spacing in the human fovea.

While attending the seminar of Maxime Dahan on Fluorescence imaging using compressed sensing, one of the audience member - I'm told it was Mickael Tanter - mentioned the time reversal kaleidoscope that has some very eery similarity with other concepts of using random materials to perform measurements like the Random Lens Imager. The paper that talks about it (behind a paywall) is The time reversal kaleidoscope: a new concept of smart transducers for 3d ultrasonic imaging by Gabriel Montaldo, Delphine Palacio, Mickael Tanter and Matthias Fink. The abstract reads:

The design of 2D arrays for 3D ultrasonic imaging is a major challenge in medical and non-destructive applications. Thousands of transducers are typically needed for beam focusing and steering in 3D volumes. Here, we report a completely new approach for producing 3D images with a small number of transducers using the combined concepts of time reversal mirrors and chaotic reverberating cavities. Due to multiple reverberations inside the cavity, a “kaleidoscopic” transducer array is created with thousands of virtual transducers equivalent to 2D matrices. Beyond the scope of 3D medical imaging, this work leads to the new concept of “smart” transducer.

It is interesting that they can do imaging in some analog fashion, I am sure that a compressive sensing step could provide a computational element that would (dramatically) enhance the resulting images and even provide some superresolution. We'll see.

As some of you know I am interested in a compressive sensing EEG system. This past week, the following interesting reference showed up on my radar screen: High-quality recording of bioelectric events. Part 1 Interference reduction, theory and practice. by A. C. Metting van Rijn A. Pepar C. A Grimbergen.

My webcrawler found the following paper published in Nature: The relationship between visual resolution and cone spacing in the human fovea by Ethan Rossi, Austin Roorda. [supplemental information] [video1][video2] [video3]. The abstract reads:

Visual resolution decreases rapidly outside of the foveal center. The anatomical and physiological basis for this reduction is unclear. We used simultaneous adaptive optics imaging and psychophysical testing to measure cone spacing and resolution across the fovea, and found that resolution was limited by cone spacing only at the foveal center. Immediately outside of the center, resolution was worse than cone spacing predicted and better matched the sampling limit of midget retinal ganglion cells.

This paper led me to another older one: Psychophysical estimate of extrafoveal cone spacing by Nancy J. Coletta and David R. Williams. The abstract reads:

In the extrafoveal retina, interference fringes at spatial frequencies higher than the resolution limit look like twodimensional spatial noise, the origin of which has not been firmly established. We show that over a limited range of high spatial frequencies this noise takes on a striated appearance, with the striations running perpendicular to the true fringe orientation. A model of cone aliasing based on anatomical measurements of extrafoveal cone position predicts that this orientation reversal should occur when the period of the interference fringe roughly equals the spacing between cones, i.e., when the fringe spatial frequency is about twice the cone Nyquist frequency. Psychophysical measurements of the orientation reversal at retinal eccentricities from 0.75 to 10 deg are in quantitative agreement with this prediction. This agreement implies that at least part of the spatial noise observed under these conditions results from aliasing by the cone mosaic. The orientation reversal provides a psychophysical method for estimating spacing in less regular mosaics, complementing another psychophysical technique for measuring spacing in the more regular mosaic of foveal cones [D. R. Williams, Vision Res. 25, 195 (1985); Vision Res. (submitted)].

In it one can read:

Previously, Yellott16 had proposed that disorder of the cone lattice prevents aliasing by smearing high spatial frequencies into broadband noise. The present data confirm that, although the aliasing noise is indeed smeared, it is still accessible to psychophysical observation. In fact, this aliasing noise can be used to draw inferences about the spacing of cones.

In light of this entry on Tilings, Islamic Art, Our Retina, Papoulis Sub-Nyquist Theorem, I had talked to Austin Roorda but never made that discussion into a blog entry. I am such a putz. I should unearth it sometimes.

Credit: NASA / JPL, pale blue dot, earth as seen from Voyager.