Improved robustness of target location in nonhomogeneous backgrounds by use of the maximum-likelihood ratio test location algorithm

A Theoretical High-Density Nanoscopy Study Leads to the Design of UNLOC, a Parameter-free Algorithm

Single-molecule localization microscopy (SMLM) enables the production of high-resolution images by imaging spatially isolated fluorescent particles. Although challenging, the result of SMLM analysis lists the position of individual molecules, leading to a valuable quantification of the stoichiometry and spatial organization of molecular actors. Both the signal/noise ratio and the density (D_frame), i.e., the number of fluorescent particles per μm² per frame, have previously been identified as determining factors for reaching a given SMLM precision. Establishing a comprehensive theoretical study relying on these two parameters is therefore of central interest to delineate the achievable limits for accurate SMLM observations. Our study reports that in absence of prior knowledge of the signal intensity α, the density effect on particle localization is more prominent than that anticipated from theoretical studies performed at known α. A first limit appears when, under a low-density hypothesis (i.e., one-Gaussian fitting hypothesis), any fluorescent particle distant by less than ∼600 nm from the particle of interest biases its localization. In fact, all particles should be accounted for, even those dimly fluorescent, to ascertain unbiased localization of any surrounding particles. Moreover, even under a high-density hypothesis (i.e., multi-Gaussian fitting hypothesis), a second limit arises because of the impossible distinction of particles located too closely. An increase in D_frame is thus likely to deteriorate the localization precision, the image reconstruction, and more generally the quantification accuracy. Our study firstly provides a density-signal/noise ratio space diagram for use as a guide in data recording toward reaching an achievable SMLM resolution. Additionally, it leads to the identification of the essential requirements for implementing UNLOC, a parameter-free and fast computing algorithm approaching the Cramér-Rao bound for particles at high-density per frame and without any prior knowledge of their intensity. UNLOC is available as an ImageJ plugin.

Three dimensional object recognition with photon counting imagery in the presence of noise

Three dimensional (3D) imaging systems have been recently suggested for passive sensing and recognition of objects in photon-starved environments where only a few photons are emitted or reflected from the object. In this paradigm, it is important to make optimal use of limited information carried by photons. We present a statistical framework for 3D passive object recognition in presence of noise. Since in quantum-limited regime, detector dark noise is present, our approach takes into account the effect of noise on information bearing photons. The model is tested when background noise and dark noise sources are present for identifying a target in a 3D scene. It is shown that reliable object recognition is possible in photon-counting domain. The results suggest that with proper translation of physical characteristics of the imaging system into the information processing algorithms, photon-counting imagery can be used for object classification.

Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images

In many imaging applications, the measured optical images are perturbed by strong fluctuations or boise. This can be the case, for example, for coherent-active or low-flux imagery. In such cases, the noise is not Gaussian additive and the definition of a contrast parameter between two regions in the image is not always a straightforward task. We show that for noncorrelated noise, the Bhattacharyya distance can be an efficient candidate for contrast definition when one uses statistical algorithms for detection, location, or segmentation. We demonstrate with numerical simulations that different images with the same Bhattacharyya distance lead to equivalent values of the performance criterion for a large number of probability laws. The Bhattacharyya distance can thus be used to compare different noisy situations and to simplify the analysis and the specification of optical imaging systems.

Photon-noise effect on detection in coherent active images

We analyze photon-noise effects on target detection performance in low-flux coherent active imagery systems. We show that when photon noise is expected, the performance of classical detection techniques designed for pure and fully developed speckle images can be improved with no increase in algorithm complexity. Furthermore, the mean photon number under which photon noise becomes sensitive is higher when the target and background mean values are unknown than in the idealized case, where they are assumed to be known, and when the reflectivity ratio between the target and the background is low.

Constrained quadratic correlation filters for target detection

A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented.

Target detection with a liquid-crystal-based passive Stokes polarimeter

We present an imaging system that measures the polarimetric state of the light coming from each point of a scene. This system, which determines the four components of the Stokes vector at each spatial location, is based on a liquid-crystal polarization modulator, which makes it possible to acquire four-dimensional Stokes parameter images at a standard video rate. We show that using such polarimetric images instead of simple intensity images can improve target detection and segmentation performance.

Performance parameters for detection in low-flux coherent images

We analyze the optimization of low-flux coherent active imagery systems for target detection. We demonstrate that, unlike the Fisher ratio, the Bhattacharyya distance is an efficient figure of merit when one uses detection algorithms based on the generalized likelihood ratio test for realistic situations when the target and the background mean values are unknown. For example, we show that detection capabilities can be better if the pulse energy is divided into four shots, whereas using more than ten shots does not significantly improve the results.

Detection of objects composed of several regions by a region-configuration-estimation method

The task of detection of objects composed of several regions by means of statistical filters is analyzed. The target is assumed to have different unknown mean values in each of its regions. The detection is based on likelihood estimation, after performing an estimation of the actual configuration of the mean values in the target region. A simplified filter that reduces the computational complexity is also proposed. The statistical performance is analyzed theoretically and tested in computer experiments.

Detection of multiregion objects embedded in nonoverlapping noise

The concept of a statistical filter for objects that comprise several regions is introduced. The process is optimal in the presence of nonoverlapping noise for the target and may perform independently of variations in the mean value in every region. The basic performance of the filter is described, and a comparison with other types of processing is made.

Statistical techniques for target detection in polarization diversity images

We address the problem of target detection in active polarimetric images. This technique, which has the appealing feature of revealing contrasts that do not appear in conventional intensity images, provides several images of the same scene. However, because of the presence of nonhomogeneity in the reflected intensity, it is preferable to perform target detection on the orthogonal-state contrast image, which is a measure of the degree of polarization of the reflected light when the coherency matrix is diagonal. We show that one can determine a simple nonlinear transformation of this orthogonal-state contrast image that leads to additive noise, and we then propose a simple and efficient technique for detecting targets in these images.