Nikos P. Pitsianis

Approximation with Kronecker Products

Let A be an m-by-n matrix with m=m1m2 and n=n1n2. We consider the problem of finding (mathematical formula omitted) so that (mathematical formula omitted) is minimized. This problem can be solved by computing the largest singular value and associated singular vectors of a permuted version of A. If A is symmetric, definite, non-negative, or banded, then the minimizing B and C are similarly structured. The idea of using Kronecker product preconditioners is briefly discussed.

Video rate spectral imaging using a coded aperture snapshot spectral imager.

We have previously reported on coded aperture snapshot spectral imagers (CASSI) that can capture a full frame spectral image in a snapshot. Here we describe the use of CASSI for spectral imaging of a dynamic scene at video rate. We describe significant advances in the design of the optical system, system calibration procedures and reconstruction method. The new optical system uses a double Amici prism to achieve an in-line, direct view configuration, resulting in a substantial improvement in image quality. We describe NeAREst, an algorithm for estimating the instantaneous three-dimensional spatio-spectral data cube from CASSIs two-dimensional array of encoded and compressed measurements. We utilize CASSIs snapshot ability to demonstrate a spectral image video of multi-colored candles with live flames captured at 30 frames per second.

Thin infrared imaging systems through multichannel sampling

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide-aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3 mm and achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.

Path-dependent human identification using a pyroelectric infrared sensor and Fresnel lens arrays

This paper presents a design and development of a low power consumption, and low cost, human identification system using a pyroelectric infrared (PIR) sensor whose visibility is modulated by a Fresnel lens array. The optimal element number of the lens array for the identification system was investigated and the experimental results suggest that the lens array with more elements can yield a better performance in terms of identification and false alarm rates. The other parameters of the system configuration such as the height of sensor location and sensor-to-object distance were also studied to improve spectral distinctions among sensory data of human objects. The identification process consists of two parts: training and testing. For the data training, we employed a principal components regression (PCR) method to cluster data with respect to different registered objects at different speed levels. The feature data of different objects walking along the same path in training yet at random speeds are then tested against the pre-trained clusters to decide whether the target is registered, and which member of the registered group it is.

A Matrix Version of the Fast Multipole Method

We present a matrix interpretation of the three-dimensional fast multipole method (FMM). The FMM is for efficient computation of gravitational/electrostatic potentials and fields. It has found various applications and inspired the design of many efficient algorithms. The one-dimensional FMM is well interpreted in terms of matrix computations. The three-dimensional matrix version reveals the underlying matrix structures and computational techniques used in FMM. It also provides a unified view of algorithm variants as well as existing and emerging implementations of the FMM.

Coded apertures for efficient pyroelectric motion tracking

Coded apertures may be designed to modulate the visibility between source and measurement spaces such that the position of a source among N resolution cells may be discriminated using logarithm of N measurements. We use coded apertures as reference structures in a pyroelectric motion tracking system. This sensor system is capable of detecting source motion in one of the 15 cells uniformly distributed over a 1.6m x 1.6m domain using 4 pyroelectric detectors.

Coded Aperture Raman Spectroscopy for Quantitative Measurements of Ethanol in a Tissue Phantom

Coded aperture spectroscopy allows for sources of large étendue to be efficiently coupled into dispersive spectrometers by replacing the traditional input slit with a patterned mask. We describe a coded aperture spectrometer optimized for Raman spectroscopy of diffuse sources, (e.g., tissue). We provide design details of the Raman system, along with quantitative estimation results for ethanol at non-toxic levels in a lipid tissue phantom. With 60 mW of excitation power at 808 nm, leave-one-out and blind cross-validation of partial least squares (PLS) regression models achieve r2 > 0.98. Leave-one-out cross-validation demonstrates prediction errors of < 15% at the common legal limit for intoxication (17.4 mmol/L = 0.08% by vol) and the best blind cross-validation achieves < 12% error at this concentration.

Parallel search of k-nearest neighbors with synchronous operations

We present a new study of parallel algorithms for locating k-nearest neighbors (kNN) of each single query in a high dimensional (feature) space on a many-core processor or accelerator that favors synchronous operations, such as on a graphics processing unit. Exploiting the intimate relationships between two primitive operations, select and sort, we introduce a cohort of truncated sort algorithms for parallel kNN search. The truncated bitonic sort (TBiS) in particular has desirable data locality, synchronous concurrency and simple data and program structures. Its implementation on a graphics processing unit outperforms the other existing implementations for kNN search based on either sort or select operations. We provide algorithm analysis and experimental results.

Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers

This paper describes numerical estimation techniques for coded aperture snapshot spectral imagers (CASSI). In a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation of both spectral information and 2D spatial information of a scene. The spatial information is modulated by a coded aperture and the spectral information is modulated by a dispersive element. The estimation process decodes the 2D measurements to render a three-dimensional spatio-spectral estimate of the scene, and is therefore an indispensable component of the spectral imager. Numerical estimation results are presented.

Reference structure tomography

Reference structure tomography (RST) uses multidimensional modulations to encode mappings between radiating objects and measurements. RST may be used to image source-density distributions, estimate source parameters, or classify sources. The RST paradigm permits scan-free multidimensional imaging, data-efficient and computation-efficient source analysis, and direct abstraction of physical features. We introduce the basic concepts of RST and illustrate the use of RST for multidimensional imaging based on a geometric radiation model.