Minimum-mean-square-error filters for detecting a noisy target in background noise

Methods to detect objects in photon-limited images

We investigate the problem of detecting and localizing a known signal in a photon-limited image, where Poisson noise is the dominant source of image degradation. For this purpose we developed and evaluated three new algorithms. The first two are based on the impulse restoration (IR) principle and the third is based on the generalized likelihood ratio test (GLRT). In the IR approach, the problem is formulated as one of restoring a delta function at the location of the desired object. In the GLRT approach, which is a well-known variation on the optimal likelihood ratio test, the problem is formulated as a hypothesis testing problem, in which the unknown background intensity of the image and the intensity scale of the object are obtained by maximum-likelihood estimation. We used Monte Carlo simulations and localization receiver operating characteristic (LROC) curves to evaluate the proposed algorithms quantitatively. LROC curves demonstrate the ability of an algorithm to detect and locate objects in a scene correctly. Our simulations demonstrate that the GLRT approach is superior to all other tested algorithms.

Pattern recognition with a digital holographic microscope working in partially coherent illumination

We describe the implementation of the automatic spatial-frequency-selection filter for recognition of patterns obtained with a digital holographic microscope working with a partially coherent source. The microscope provides the complex-optical-amplitude field that allows a refocusing plane-by-plane of the sample under investigation by numerical computation of the optical propagation. By inserting a correlation filter in the propagation equation, the correlation between the filter and the propagated optical field is obtained. In this way, the pattern is located in the direction of the optical axis. Owing to the very weak noise level generated by the partially coherent source, the correlation process is shift invariant. Therefore the samples can be located in the three dimensions. To have a robust recognition process, a generalized version of the automatic spatial-frequency-selection filters has been implemented. The method is experimentally demonstrated in a two-class problem for the recognition of protein crystals.

Reduction of the correlation sensitivity to the changes of the input illumination by a post processing based on the correlation statistics

Linear-correlation amplitude changes when the intensity level of the input image is modified. As recognition is often based on the correlation-peak level, a change of the input illumination may result in a false recognition. We propose an illumination-change compensation by a post processing of the correlation distribution that is based on statistical measures of the correlation histograms. The theoretical background and simulation results are provided in the frame of an actual application in biology.

Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition

Matched filtering followed by a minimum Euclidean distance projection onto realizable filter values was previously shown to optimize the signal-to-noise ratio for single training images in optical correlation pattern recognition. The algorithm is now shown to solve the combination of (1) standard statistical pattern-recognition metrics with multiple training images, (2) additive input noise of known power spectral density and also additive detection noise that is irreducible by the filter, (3) the building of the filter on arbitrary subsets of the complex unit disk, and (4) the use of observable correlator outputs only. The criteria include the Fisher ratio, the Bayes error and Bayes cost, the Chernoff and Bhattacharyya bounds, the population entropy and expected information, versions of signal-to-noise ratio that use other than second power in their norm, and the area under the receiver operating characteristic curve. Different criteria are optimized by different complex scalar weights.