CS: SPIE meeting, Lensless wide-field fluorescent imaging, Compressive sensor networks, Multichannel Sampling RI, ECME Thresholding Methods.

You'd thought you'd go home with nothing to read. Fear not, it's not happening this week-end:

Stefano Marchesini let me know of the following SPIE meeting with several compressive sensing papers in them.

Hi Igor,
there are a few talks on compressive sensing in the following spie conference:
http://spie.org//app/program/index.cfm?fuseaction=conferencedetail&conference=7800

Thanks Stefano.

Today, we have some new hardware: Lensless wide-field fluorescent imaging on a chip using compressive decoding of sparse objects by Ahmet F. Coskun, Ikbal Sencan, Ting-Wei Su, and Aydogan Ozcan. The abstract reads:

We demonstrate the use of a compressive sampling algorithm for on-chip fluorescent imaging of sparse objects over an ultra-large field-of-view (>8 cm2) without the need for any lenses or mechanical scanning. In this lensfree imaging technique, fluorescent samples placed on a chip are excited through a prism interface, where the pump light is filtered out by total internal reflection after exciting the entire sample volume. The emitted fluorescent light from the specimen is collected through an on-chip fiber-optic faceplate and is delivered to a wide field-of-view opto-electronic sensor array for lensless recording of fluorescent spots corresponding to the samples. A compressive sampling based optimization algorithm is then used to rapidly reconstruct the sparse distribution of fluorescent sources to achieve ~10 µm spatial resolution over the entire active region of the sensor-array, i.e., over an imaging field-of-view of >8 cm2. Such a wide-field lensless fluorescent imaging platform could especially be significant for high-throughput imaging cytometry, rare cell analysis, as well as for micro-array research.

I'll add it shortly to the compressive sensing hardware page.

John Zheng Sun's thesis at MIT entitled: Compressive sensor networks : fundamental limits and algorithms is out. The abstract reads:

Compressed sensing is a non-adaptive compression method that takes advantage of natural sparsity at the input and is fast gaining relevance to both researchers and engineers for its universality and applicability. First developed by Candis et al., the subject has seen a surge of high-quality results both in its theory and applications. This thesis extends compressed sensing ideas to sensor networks and other bandwidth-constrained communication systems. In particular, we explore the limits of performance of compressive sensor networks in relation to fundamental operations such as quantization and parameter estimation. Since compressed sensing is originally formulated as a real-valued problem, quantization of the measurements is a very natural extension. Although several researchers have proposed modified reconstruction methods that mitigate quantization noise for a fixed quantizer, the optimal design of such quantizers is still unknown. We propose to find the optimal quantizer in terms of minimizing quantization error by using recent results in functional scalar quantization. The best quantizer in this case is not the optimal design for the measurements themselves but rather is reweighted by a factor we call the sensitivity. Numerical results demonstrate a constant-factor improvement in the fixed-rate case. Parameter estimation is an important goal of many sensing systems since users often care about some function of the data rather than the data itself. Thus, it is of interest to see how efficiently nodes using compressed sensing can estimate a parameter, and if the measurements scalings can be less restrictive than the bounds in the literature. We explore this problem for time difference and angle of arrival, two common methods for source geolocation. We first derive Cramer-Rao lower bounds for both parameters and show that a practical block-OMP estimator can be relatively efficient for signal reconstruction. However, there is a large gap between theory and practice for time difference or angle of arrival estimation, which demonstrates the CRB to be an optimistic lower bound for nonlinear estimation. We also find scaling laws 'for time difference estimation in the discrete case. This is strongly related to partial support recovery, and we derive some new sufficient conditions that show a very simple reconstruction algorithm can achieve substantially better scaling than full support recovery suggests is possible.

Multichannel Sampling of Pulse Streams at the Rate of Innovation by Kfir Gedalyahu, Ronen Tur, Yonina Eldar. The abstract reads:

We consider minimal-rate sampling schemes for streams of delayed and weighted versions of a known pulse shape. Such signals belong to the class of finite rate of innovation (FRI) models. The minimal sampling rate for these parametric signals, is the number of degrees of freedom per unit of time, referred to as the rate of innovation. Although sampling of pulse streams was treated in previous works, either the rate of innovation was not achieved, or the pulse shape was limited to diracs and the method was instable for high rates of innovation. In this work we propose a multichannel framework for pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches.

ECME Thresholding Methods for Sparse Signal Reconstruction by Kun Qiu, Aleksandar Dogandzic. The abstract reads:

We propose a probabilistic framework for interpreting and developing hard thresholding sparse signal reconstruction methods and present several new algorithms based on this framework. The measurements follow an underdetermined linear model, where the regression-coefficient vector is the sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. We first derive an expectation-conditional maximization either (ECME) iteration that guarantees convergence to a local maximum of the likelihood function of the unknown parameters for a given signal sparsity level. To analyze the reconstruction accuracy, we introduce the minimum sparse subspace quotient (SSQ), a more flexible measure of the sampling operator than the well-established restricted isometry property (RIP). We prove that, if the minimum SSQ is sufficiently large, ECME achieves perfect or near-optimal recovery of sparse or approximately sparse signals, respectively. We also propose a double overrelaxation (DORE) thresholding scheme for accelerating the ECME iteration. If the signal sparsity level is unknown, we introduce an unconstrained sparsity selection (USS) criterion for its selection and show that, under certain conditions, applying this criterion is equivalent to finding the sparsest solution of the underlying underdetermined linear system. Finally, we present our automatic double overrelaxation (ADORE) thresholding method that utilizes the USS criterion to select the signal sparsity level. We apply the proposed schemes to reconstruct sparse and approximately sparse signals from tomographic projections and compressive samples.