Lensless wide-field fluorescent imaging on a chip using compressive decoding of sparse objects.

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 cm(2)) 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 approximately 10 microm spatial resolution over the entire active region of the sensor-array, i.e., over an imaging field-of-view of >8 cm(2). 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

Structured random measurements in signal processing

Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples. While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices. Near optimal recovery guarantees for such structured measurements have been developed over the past years in a variety of contexts. This article surveys the theory in three scenarios: compressed sensing (sparse recovery), low rank matrix recovery, and phaseless estimation. The random measurement matrices to be considered include random partial Fourier matrices, partial random circulant matrices (subsampled convolutions), matrix completion, and phase estimation from magnitudes of Fourier type measurements. The article concludes with a brief discussion of the mathematical techniques for the analysis of such structured random measurements.Comment: 22 pages, 2 figure

Compressive Sensing Theory for Optical Systems Described by a Continuous Model

A brief survey of the author and collaborators' work in compressive sensing applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern published by Taylor & Francis 201

Compressed sensing performance bounds under Poisson noise

This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this setting, standard CS techniques cannot be applied directly for several reasons. First, the usual signal-independent and/or bounded noise models do not apply to Poisson noise, which is non-additive and signal-dependent. Second, the CS matrices typically considered are not feasible in real optical systems because they do not adhere to important constraints, such as nonnegativity and photon flux preservation. Third, the typical $\ell_2$--$\ell_1$ minimization leads to overfitting in the high-intensity regions and oversmoothing in the low-intensity areas. In this paper, we describe how a feasible positivity- and flux-preserving sensing matrix can be constructed, and then analyze the performance of a CS reconstruction approach for Poisson data that minimizes an objective function consisting of a negative Poisson log likelihood term and a penalty term which measures signal sparsity. We show that, as the overall intensity of the underlying signal increases, an upper bound on the reconstruction error decays at an appropriate rate (depending on the compressibility of the signal), but that for a fixed signal intensity, the signal-dependent part of the error bound actually grows with the number of measurements or sensors. This surprising fact is both proved theoretically and justified based on physical intuition.Comment: 12 pages, 3 pdf figures; accepted for publication in IEEE Transactions on Signal Processin

Roadmap on optical security

Postprint (author's final draft