Amit Ashok

Task-specific information for imaging system analysis

Imagery is often used to accomplish some computational task. In such cases there are some aspects of the imagery that are relevant to the task and other aspects that are not. In order to quantify the task-specific quality of such imagery, we introduce the concept of task-specific information (TSI). A formal framework for the computation of TSI is described and is applied to three common tasks: target detection, classification, and localization. We demonstrate the utility of TSI as a metric for evaluating the performance of three imaging systems: ideal geometric, diffraction-limited, and projective. The TSI results obtained from the simulation study quantify the degradation in the task-specific performance with optical blur. We also demonstrate that projective imagers can provide higher TSI than conventional imagers at small signal-to-noise ratios.

Compressive imaging system design using task-specific information

We present a task-specific information (TSI) based framework for designing compressive imaging (CI) systems. The task of target detection is chosen to demonstrate the performance of the optimized CI system designs relative to a conventional imager. In our optimization framework, we first select a projection basis and then find the associated optimal photon-allocation vector in the presence of a total photon-count constraint. Several projection bases, including principal components (PC), independent components, generalized matched-filter, and generalized Fisher discriminant (GFD) are considered for candidate CI systems, and their respective performance is analyzed for the target-detection task. We find that the TSI-optimized CI system design based on a GFD projection basis outperforms all other candidate CI system designs as well as the conventional imager. The GFD-based compressive imager yields a TSI of 0.9841 bits (out of a maximum possible 1 bit for the detection task), which is nearly ten times the 0.0979 bits achieved by the conventional imager at a signal-to-noise ratio of 5.0. We also discuss the relation between the information-theoretic TSI metric and a conventional statistical metric like probability of error in the context of the target-detection problem. It is shown that the TSI can be used to derive an upper bound on the probability of error that can be attained by any detection algorithm.

Pseudorandom phase masks for superresolution imaging from subpixel shifting

We present a method for overcoming the pixel-limited resolution of digital imagers. Our method combines optical point-spread function engineering with subpixel image shifting. We place an optimized pseudorandom phase mask in the aperture stop of a conventional imager and demonstrate the improved performance that can be achieved by combining multiple subpixel shifted images. Simulation results show that the pseudorandom phase-enhanced lens (PRPEL) imager achieves as much as 50% resolution improvement over a conventional multiframe imager. The PRPEL imager also enhances reconstruction root-mean-squared error by as much as 20%. We present experimental results that validate the predicted PRPEL imager performance.

Compressive imaging: hybrid measurement basis design

The inherent redundancy in natural scenes forms the basis of compressive imaging where the number of measurements is less than the dimensionality of the scene. The compressed sensing theory has shown that a purely random measurement basis can yield good reconstructions of sparse objects with relatively few measurements. However, additional prior knowledge about object statistics that is typically available is not exploited in the design of the random basis. In this work, we describe a hybrid measurement basis design that exploits the power spectral density statistics of natural scenes to minimize the reconstruction error by employing an optimal combination of a nonrandom basis and a purely random basis. Using simulation studies, we quantify the reconstruction error improvement achievable with the hybrid basis for a diverse set of natural images. We find that the hybrid basis can reduce the reconstruction error up to 77% or equivalently requires fewer measurements to achieve a desired reconstruction error compared to the purely random basis. It is also robust to varying levels of object sparsity and yields as much as 40% lower reconstruction error compared to the random basis in the presence of measurement noise.

Compressive light field imaging

Light field imagers such as the plenoptic and the integral imagers inherently measure projections of the four dimensional (4D) light field scalar function onto a two dimensional sensor and therefore, suffer from a spatial vs. angular resolution trade-off. Programmable light field imagers, proposed recently, overcome this spatioangular resolution trade-off and allow high-resolution capture of the (4D) light field function with multiple measurements at the cost of a longer exposure time. However, these light field imagers do not exploit the spatio-angular correlations inherent in the light fields of natural scenes and thus result in photon-inefficient measurements. Here, we describe two architectures for compressive light field imaging that require relatively few photon-efficient measurements to obtain a high-resolution estimate of the light field while reducing the overall exposure time. Our simulation study shows that, compressive light field imagers using the principal component (PC) measurement basis require four times fewer measurements and three times shorter exposure time compared to a conventional light field imager in order to achieve an equivalent light field reconstruction quality.

Cellular imaging of deep organ using two-photon Bessel light-sheet nonlinear structured illumination microscopy

In vivo fluorescent cellular imaging of deep internal organs is highly challenging, because the excitation needs to penetrate through strong scattering tissue and the emission signal is degraded significantly by photon diffusion induced by tissue-scattering. We report that by combining two-photon Bessel light-sheet microscopy with nonlinear structured illumination microscopy (SIM), live samples up to 600 microns wide can be imaged by light-sheet microscopy with 500 microns penetration depth, and diffused background in deep tissue light-sheet imaging can be reduced to obtain clear images at cellular resolution in depth beyond 200 microns. We demonstrate in vivo two-color imaging of pronephric glomeruli and vasculature of zebrafish kidney, whose cellular structures located at the center of the fish body are revealed in high clarity by two-color two-photon Bessel light-sheet SIM.

Radar Target Profiling and Recognition Based on TSI-Optimized Compressive Sensing Kernel

The design of wideband radar systems is often limited by existing analog-to-digital (A/D) converter technology. State-of-the-art A/D rates and high effective number of bits result in rapidly increasing cost and power consumption for the radar system. Therefore, it is useful to consider compressive sensing methods that enable reduced sampling rate, and in many applications, prior knowledge of signals of interest can be learned from training data and used to design better compressive measurement kernels. In this paper, we use a task-specific information-based approach to optimizing sensing kernels for high-resolution radar range profiling of man-made targets. We employ a Gaussian mixture (GM) model for the targets and use a Taylor series expansion of the logarithm of the GM probability distribution to enable a closed-form gradient of information with respect to the sensing kernel. The GM model admits nuisance parameters such as target pose angle and range translation. The gradient is then used in a gradient-based approach to search for the optimal sensing kernel. In numerical simulations, we compare the performance of the proposed sensing kernel design to random projections and to lower-bandwidth waveforms that can be sampled at the Nyquist rate. Simulation results demonstrate that the proposed technique for sensing kernel design can significantly improve performance.

Information optimal compressive sensing: static measurement design

The compressive sensing paradigm exploits the inherent sparsity/compressibility of signals to reduce the number of measurements required for reliable reconstruction/recovery. In many applications additional prior information beyond signal sparsity, such as structure in sparsity, is available, and current efforts are mainly limited to exploiting that information exclusively in the signal reconstruction problem. In this work, we describe an information-theoretic framework that incorporates the additional prior information as well as appropriate measurement constraints in the design of compressive measurements. Using a Gaussian binomial mixture prior we design and analyze the performance of optimized projections relative to random projections under two specific design constraints and different operating measurement signal-to-noise ratio (SNR) regimes. We find that the information-optimized designs yield significant, in some cases nearly an order of magnitude, improvements in the reconstruction performance with respect to the random projections. These improvements are especially notable in the low measurement SNR regime where the energy-efficient design of optimized projections is most advantageous. In such cases, the optimized projection design departs significantly from random projections in terms of their incoherence with the representation basis. In fact, we find that the maximizing incoherence of projections with the representation basis is not necessarily optimal in the presence of additional prior information and finite measurement noise/error. We also apply the information-optimized projections to the compressive image formation problem for natural scenes, and the improved visual quality of reconstructed images with respect to random projections and other compressive measurement design affirms the overall effectiveness of the information-theoretic design framework.

Object reconstruction from adaptive compressive measurements in feature-specific imaging

Static feature-specific imaging (SFSI), where the measurement basis remains fixed/static during the data measurement process, has been shown to be superior to conventional imaging for reconstruction tasks. Here, we describe an adaptive approach that utilizes past measurements to inform the choice of measurement basis for future measurements in an FSI system, with the goal of maximizing the reconstruction fidelity while employing the fewest measurements. An algorithm to implement this adaptive approach is developed for FSI systems, and the resulting systems are referred to as adaptive FSI (AFSI) systems. A simulation study is used to analyze the performance of the AFSI system for two choices of measurement basis: principal component (PC) and Hadamard. Here, the root mean squared error (RMSE) metric is employed to quantify the reconstruction fidelity. We observe that an AFSI system achieves as much as 30% lower RMSE compared to an SFSI system. The performance improvement of the AFSI systems is verified using an experimental setup employed using a digital micromirror device (DMD) array.

Information-based analysis of simple incoherent imaging systems.

We present an information-based analysis of three candidate imagers: a conventional lens system, a cubic phase mask system, and a random phase mask system. For source volumes comprising relatively few equal-intensity point sources we compare both the axial and lateral information content of detector intensity measurements. We include the effect of additive white Gaussian noise. Single and distributed aperture imaging is studied. A single detector in each of two apertures using conventional lenses can yield 36% of the available scene information when the source volume contains only single point source. The addition of cubic phase masks yields nearly 74% of the scene information. An identical configuration using random phase masks offers the best performance with 89% scene information available in the detector intensity measurements.