SignificanceThe emergence of label-free microscopy techniques has significantly improved our ability to precisely characterize biochemical targets, enabling non-invasive visualization of cellular organelles and tissue organization. However, understanding each label-free method with respect to the specific benefits, drawbacks, and varied sensitivities under measurement conditions across different types of specimens remains a challenge.AimWe link all of these disparate label-free optical interactions together and compare the detection sensitivity within the framework of statistical estimation theory.ApproachTo achieve this goal, we introduce a comprehensive unified framework for evaluating the bounds for signal detection with label-free microscopy methods, including second-harmonic generation, third-harmonic generation, coherent anti-Stokes Raman scattering, coherent Stokes Raman scattering, stimulated Raman loss, stimulated Raman gain, stimulated emission, impulsive stimulated Raman scattering, transient absorption, and photothermal effect. A general model for signal generation induced by optical scattering is developed.ResultsBased on this model, the information obtained is quantitatively analyzed using Fisher information, and the fundamental constraints on estimation precision are evaluated through the Cramér–Rao lower bound, offering guidance for optimal experimental design and interpretation.ConclusionsWe provide valuable insights for researchers seeking to leverage label-free techniques for non-invasive imaging applications for biomedical research and clinical practice.
Imaging of the interior of object with light has long been a challenge for optical imaging. Optical diffraction tomography (ODT) is able to obtain three-dimensional (3D) object information through object rotation. We will discuss harmonic optical tomography (HOT) that exploits a defocused illumination beam for nonlinear optical tomography. We will also discuss our demonstration of coherent ODT with incoherent light emission in a new optical tomography technique called fluorescent diffraction tomography (FDT) and the use of spatial frequency imaging for high speed nonlinear optical microscopy.
Single-pixel imaging is a developing family of techniques
which offer several advantages over conventional imaging with a segmented detector.
These include higher speed, improved availability and quality
of detectors at long wavelengths.
Examples include laser-scanning microscopy,
frequency-domain techniques, ghost imaging,
and methods employing an orthogonal mask sequence such as Hadamard masks.
We analyze this class of imaging techniques in terms of Frame theory,
which concerns sets of vectors that span a given vector space
but are not linearly independent as in the case of a basis.
The use of frames (rather than bases) allows for redundant measurements,
which can improve the signal-to-noise ratio (SNR) of the reconstructed image.
Current single-pixel techniques
admit an intuitive, physically-motivated reconstruction scheme,
but the reconstruction method is not always obvious.
The analysis provides a prescription
for reconstruction with any single-pixel imaging scheme.
For example, illumination with speckle-like patterns
which lack the statistical properties associated with speckle
does not allow accurate reconstruction with conventional methods,
but frame theory-inspired analysis allows
production of high-contrast, diffraction-limited images.
Even for schemes where reconstruction methods exist,
the theory can improve contrast, accuracy and resolution.
Frame theory-motivated reconstruction from simulated ghost imaging data
results in markedly improved contrast,
and resolution.
This analysis makes viable new single-pixel techniques
which lack intuitive reconstruction strategies,
and tuning of imaging properties such as noise for specific applications.
Many single-pixel imaging techniques have been developed in recent years. Though the methods of image acquisition vary considerably, the methods share unifying features that make general analysis possible. Furthermore, the methods developed thus far are based on intuitive processes that enable simple and physically-motivated reconstruction algorithms, however, this approach may not leverage the full potential of single-pixel imaging. We present a general theoretical framework of single-pixel imaging based on frame theory, which enables general, mathematically rigorous analysis. We apply our theoretical framework to existing single-pixel imaging techniques, as well as provide a foundation for developing more-advanced methods of image acquisition and reconstruction. The proposed frame theoretic framework for single-pixel imaging results in improved noise robustness, decrease in acquisition time, and can take advantage of special properties of the specimen under study. By building on this framework, new methods of imaging with a single element detector can be developed to realize the full potential associated with single-pixel imaging.
We study the performance of modal analysis using sparse linear arrays (SLAs) such as nested and co-prime arrays, in both first-order and second-order measurement models. We treat SLAs as constructed from a subset of sensors in a dense uniform linear array (ULA), and characterize the performance loss of SLAs with respect to the ULA due to using much fewer sensors. In particular, we claim that, provided the same aperture, in order to achieve comparable performance in terms of Cramér-Rao bound (CRB) for modal analysis, SLAs require more snapshots, of which the number is about the number of snapshots used by ULA times the compression ratio in the number of sensors. This is shown analytically for the case with one undamped mode, as well as empirically via extensive numerical experiments for more complex scenarios. Moreover, the misspecified CRB proposed by Richmond and Horowitz is also studied, where SLAs suffer more performance loss than their ULA counterpart.
Anti-virus software based on unsupervised hierarchical clustering (HC) of malware samples has been shown to be vulnerable to poisoning attacks. In this kind of attack, a malicious player degrades anti-virus performance by submitting to the database samples specifically designed to collapse the classification hierarchy utilized by the anti-virus (and constructed through HC) or otherwise deform it in a way that would render it useless. Though each poisoning attack needs to be tailored to the particular HC scheme deployed, existing research seems to indicate that no particular HC method by itself is immune. We present results on applying a new notion of entropy for combinatorial dendrograms to the problem of controlling the influx of samples into the data base and deflecting poisoning attacks. In a nutshell, effective and tractable measures of change in hierarchy complexity are derived from the above, enabling on-the-fly flagging and rejection of potentially damaging samples. The information-theoretic underpinnings of these measures ensure their indifference to which particular poisoning algorithm is being used by the attacker, rendering them particularly attractive in this setting.
A fusion frame is a frame-like collection of subspaces in a Hilbert space. It generalizes the concept of a frame
system for signal representation. In this paper, we study the existence and construction of fusion frames. We first
introduce two general methods, namely the spatial complement and the Naimark complement, for constructing a
new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired
properties. In particular, we address the following question: Given M, N, m ∈ N and {λj}Mj
=1, does there exist
a fusion frame in RM with N subspaces of dimension m for which {λj}Mj
=1 are the eigenvalues of the associated
fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame
for almost any collection of parameters M, N, m ∈ N and {λj}Mj
=1. Moreover, we show how this procedure can
be applied, if subspaces are to be added to a given fusion frame to force it to become tight.
We present a new receiver design for spatially distributed
apertures to detect targets in an urban environment.
A distorted-wave Born approximation is used to model the scattering
environment. We formulate the received signals at different
receive antennas in terms of the received signal at the first
antenna. The detection problem is then formulated as a binary
hypothesis test. The receiver is chosen as the optimal linear filter
that maximizes the signal-to-noise ratio (SNR) of the
corresponding test statistic. The receiver operation amounts to
correlating a transformed version of the measurement at the first
antenna with the rest of the measurements. In the
free-space case the transformation applied to the measurement from the
first
antenna reduces to a delay operator. We evaluate the performance of
the receiver on a real data set collected in a multipath- and
clutter-rich urban environment and on simulated data corresponding to a simple
multipath scene. Both the experimental and simulation results show that
the proposed receiver design offers significant improvement in
detection performance compared to conventional matched
filtering.
Various sparse array configurations have been studied to improve
spatial resolution for separating several closely spaced targets in
tight formations using unattended acoustic arrays. To extend the
array aperture, it is customary to employ sparse array
configurations with uniform inter-array spacing wider than the
half-wavelength intra-subarray spacing, hence achieving more
accurate direction of arrival (DOA) estimates without using extra
hardware. However, this larger inter-array positioning results in
ambiguous DOA estimates. To resolve this ambiguity, sparse arrays
with multiple invariance properties could be deployed.
Alternatively, one can design regular or random sparse array
configurations that provide frequency diversity, in which case every
subarray is designed for a particular band of frequencies. These
different configurations are investigated in this paper.
Additionally, we present a Capon DOA algorithm that exploits the
specific geometry of each array configuration. Simulation results
are presented to study the pros and cons of different sparse
configurations.
A feature extraction method for underwater target classification
is developed that exploits the linear dependence (coherence)
between two sonar returns. A canonical coordinate decomposition is
applied to resolve two consecutive acoustic backscattered signals
into their dominant canonical coordinates. The corresponding
canonical correlations are selected as features for classifying
mine-like from non-mine-like objects. Test results are based on a
subset of a wideband data set that has been collected at the
Applied Research Lab (ARL), University of Texas (UT)-Austin. This
subset includes returns from different mine-like and non-mine-like
objects at several aspect angles in a smooth bottom condition. The
test results demonstrate the potential of the canonical
correlation-based feature extraction for underwater target
classification and indicate that canonical correlation features
are indeed robust to variations in aspect angle.
Sparse array processing methods are typically used to improve the
spatial resolution of sensor arrays for the estimation of
direction of arrival (DOA). The fundamental assumption behind
these methods is that signals that are received by the sparse
sensors (or a group of sensors) are coherent. However, coherence
may vary significantly with the changes in environmental, terrain,
and, operating conditions. In this paper canonical correlation
analysis is used to study the variations in coherence between
pairs of sub-arrays in a sparse array problem. The data set for
this study is a subset of an acoustic signature data set, acquired
from the US Army TACOM-ARDEC, Picatinny Arsenal, NJ. This data set
is collected using three wagon-wheel type arrays with five
microphones. The results show that in nominal operating
conditions, i.e. no extreme wind noise or masking effects by
trees, building, etc., the signals collected at different sensor
arrays are indeed coherent even at distant node separation.
The problem of detection, tracking and localization of multiple
wideband sources (ground vehicles) using unattended passive
acoustic sensors is considered in this paper. Existing methods
typically fail to detect, resolve and track multiple closely
spaced sources in tight formations, especially in the presence of
clutter and wind noise. In this paper, several existing wideband
direction of arrival (DOA) estimation algorithms are extended and
applied to this problem. A modified version of the Steered
Covariance Matrix (STCM) algorithm is presented that uses a
two-step search process. To overcome the problems of existing DOA
estimation methods, new wideband versions of the narrowband Capon
beamforming method are proposed that use various algorithms for
combining power spectra from different frequency bins. These
methods are then implemented and benchmarked on a real acoustic
signature data set that contains multiple ground targets moving in
tight formations.
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