This paper reports an overview of recent results in compressive imaging and detection using a single-pixel camera. These applications use a digital micromirror device to spatially modulate the light from an observed scene using binary sensing patterns. The patterns are obtained from a special Hadamard matrix that contains blocks of rows of which each has a common local signature pattern. The blocks partition the Hadamard spectrum, thus permitting analysis of the scene in terms of these local signature patterns. In contrast, Hadamard patterns are typically described in terms of their sequency, which is a global property of each individual row. The proposed local-signature, row-block point of view can be beneficial since it permits us to adaptively select the best blocks with which to sense the signal/scene of interest, or to select the best blocks based on a priori information. As a result, in imaging applications more fine-scale detail can be extracted from the scene, and in detection applications fewer false positives can result. Note, this signature row-block partitioning is a general mathematical technique that can be applied to the Kronecker product of any two matrices, of any size. For example, in our imaging application, we extend this idea to a Hadamard matrix that is not a power of two, yet whose block-signatures possess the familiar Sylvester-Walsh power-of-two sequency patterns.
The design and modeling of compressive sensing (CS) imagers is difficult due to the complexity and non-linearity of the system and reconstruction algorithm. The Night Vision Integrated Performance Model (NV-IPM) is a linear imaging system design tool that is very useful for complex system trade studies. The custom component generator, included in NV-IPM, will be used to include a recently published theory for CS that links measurement noise, easily calculated with NV-IPM, to the noise of the reconstructed CS image given the estimated sparsity of the scene and the number of measurements as input. As the sparsity will also depend on other factors such as the optical transfer function and the scene content, an empirical relationship will be developed between the linear model within NV-IPM and the non-linear reconstruction algorithm using measured test data. Using the theory, a CS imager varying the number of measurements will be compared to a notional traditional imager.
A new hyperspectral imaging system is constructed based on the idea of compressive sensing (CS). The compressed
hyperspectral measurements are acquired and unmixed directly with the proposed algorithm which determines the
abundance fractions of endmembers, completely bypassing high-complexity tasks involving the hyperspectral data cube
itself. Without the intermediate stage of 3D hyper-cube processing, data reconstruction and unmixing are combined into
a single step of much lower complexity. We assume that the involved endmembers' signatures are known and given,
from which we then directly compute abundances. We also extend this approach to blind unmixing where endmembers'
signatures are not precisely known a priori.
Building on the mathematical breakthroughs of compressive sensing (CS), we developed a 2D spectrometer system that
incorporates a spatial light modulator and a single detector. For some wavelengths outside the visible spectrum, when it
is too expensive to produce the large detector arrays, this scheme gives us a better solution by using only one pixel.
Combining this system with the "smashed filter" technique, we hope to create an efficient IR gas sensor. We performed
Matlab simulations to evaluate the effectiveness of the smashed filter for gas tracing.
The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible
image or signal from a small set of linear, non-adaptive (even random) projections. However, in
many applications, including object and target recognition, we are ultimately interested in making
a decision about an image rather than computing a reconstruction. We propose here a framework
for compressive classification that operates directly on the compressive measurements without first
reconstructing the image. We dub the resulting dimensionally reduced matched filter the smashed
filter. The first part of the theory maps traditional maximum likelihood hypothesis testing into the
compressive domain; we find that the number of measurements required for a given classification
performance level does not depend on the sparsity or compressibility of the images but only on
the noise level. The second part of the theory applies the generalized maximum likelihood method
to deal with unknown transformations such as the translation, scale, or viewing angle of a target
object. We exploit the fact the set of transformed images forms a low-dimensional, nonlinear
manifold in the high-dimensional image space. We find that the number of measurements required
for a given classification performance level grows linearly in the dimensionality of the manifold but
only logarithmically in the number of pixels/samples and image classes. Using both simulations
and measurements from a new single-pixel compressive camera, we demonstrate the effectiveness
of the smashed filter for target classification using very few measurements.
Compressive Sensing is an emerging field based on the revelation that a small number of linear projections of a compressible signal contain enough information for reconstruction and processing. It has many promising implications and enables the design of new kinds of Compressive Imaging systems and cameras. In this paper, we develop a new camera architecture that employs a digital micromirror array to perform optical calculations of linear projections of an image onto pseudorandom binary patterns. Its hallmarks include the ability to obtain an image with a single detection element while sampling the image fewer times than the number of pixels. Other attractive properties include its universality, robustness, scalability, progressivity, and computational asymmetry. The most intriguing feature of the system is that, since it relies on a single photon detector, it can be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers.
We have succeeded in adsorbing individual C60 molecules onto the tunneling region of an STM tip. The individual tip- adsorbed molecules are imaged by scanning the fullerene- adsorbed tip over a defect covered graphite surface. The nanometer-size defects serve as a surface tip array which 'inverse images' the molecules adsorbed to the tip when the surface is scanned. These tips were subsequently used to observe threefold symmetric electron scattering from point defects on a graphite surface, an effect that could not be observed using bare metal tips. Functionalizing an STM tip with an appropriate molecule adsorbate alters the density of states near the Fermi level of the tip and changes its imaging characteristics.