A method is presented for identifying buried objects using electromagnetic induction metal detectors. The method uses a physics based model for identifying two basis functions that fundamentally compose metal detector signals. These bases form a signal subspace that contains the signals from all objects at the same depth regardless of their shape, size, or metal content. First, an algorithm for determining this subspace is presented. Then utilizing the proper signal subspace, the shape of the object is determined by estimating the object's directional polarizablity.
Landmine data for electromagnetic induction (EMI) and ground penetrating radar (GPR) sensors has been collected in two background environments. The first environment is clay and the second is gravel. A multi-modal detection algorithm that utilizes a Maximum A Posteriori (MAP) approach is applied to the clay background data and compared to a pair of similar MAP detectors that utilize only the single sensors. It is shown that the multi-modal detector is more powerful than both single mode detectors regardless of landmine type. The detectors are then applied to the data from the gravel background. It is shown that a more powerful performance is achieved if the MAP detector adapts to the statistics of the new background rather than training it a priori with broader statistics that encompass both environmental conditions.
A method known as active sensing is applied to the problem of landmine detection. The platform utilizes two scanning sensor arrays composed of ground penetrating radar (GPR) and electromagnetic induction (EMI) metal detectors. Six simulated confirmation sensors are then dynamically deployed according to their ability to enhance information gain. Objects of interest are divided into ten class types: three classes are for metal landmines, three classes for plastic landmines, three classes for clutter objects, and one final class for background clutter. During the initial scan mode, a uniform probability is assumed for the ten classes. The scanning measurement assigns an updated probability based on the observations of the scanning sensors. At this point a confirmation sensor is chosen to re-interrogate the object. The confirmation sensor used is the one expected to produce the maximum information gain. A measure of entropy called the Renyi divergence is applied to the class probabilities to predict the information gain for each sensor. A time monitoring extension to the approach keeps track of time, and chooses the confirmation sensor based on a combination of maximum information gain and fastest processing time. Confusion matrices are presented for the scanning sensors showing the initial classification capability. Subsequent confusion matrices show the classification performance after applying active sensing myopically and with the time monitoring extension.
A characteristic of vehicle-based ground-penetrating radar is the hyperbolic signature generated by targets such as landmines. The hyperbola provides a significantly different shape from most false alarms. Here an approach is introduced that seeks to utilize all of the energy contained in this characteristic hyperbolic signature. We propose a Hyperbola Flattening Transform (HFT) that transforms hyperbolic signatures of interest into straight lines, which are in turn detected using the Radon transform. The algorithm is applied to both simulated and real data. Encouraging results are presented when applying the HFT to the problem of detecting low signal-to-noise ratio plastic mines.
Ground penetrating radar (GPR) has been shown to be useful in the detection of landmines. It is of great interest to extend this capability to discrimination between landmines and other objects cluttering the battlefield environment. Wavenumber migration processing (SAR imaging) is used here to show the ability of a GPR to determine both burial depth and size of landmines. Wavenumber migration imaging is summarized and an automated algorithm for extracting size and depth is introduced. A repeatability study is presented for ten signatures from the same metallic landmine. An example of 2D wavenumber migration imaging is presented, as well as, a summary of landmine size and depth estimates from the ten signatures.
3-D images obtained from optical sectioning microscopy are usually degraded by a point-spread function that is known to be an even function but is otherwise only approximately known, or even entirely unknown. We present a new algorithm for 3-D blind deconvolution of even point-spread functions that is both fast and (in the absence of noise) exact. Fourier transforms decouple the problem into 2-D, then 1-D blind deconvolution problems, greatly increasing computational speed. Numerical simulations demonstrate that the blind algorithm seems to perform both faster and more accurately than the non-blind iterative Lucy-Richardson algorithm.
The problem of 2-D blind deconvolution is to reconstruct an unknown image from its 2-D convolution with an unknown blur function. Motivated by the superior restoration quality achieved by the recently proposed nullspace-based multichannel image restoration methods, we propose a single-blur restoration approach that avoids the restrictive assumption of multichannel blurring and has the advantage of lower complexity. The assumption made about the image and the blur function is that they both have a finite spatial extent with that of the image being known. Also, the blur is assumed to be either separable or low-rank. If the blur is separable the image can be restored perfectly under noiseless conditions. When the blur is low-rank, favorable results can be achieved if the blur function has large spatial extent relative to the image. This requirement makes the proposed solution suitable for the cases where the degraded images are severely blurred.
Superresolution is the problem of reconstructing a single high-resolution image from several blurred and downsampled low-resolution versions of it. We solve this problem for the case of unknown blurring functions. The image and functions must have finite support, and the number of low-resolution images must equal or exceed the number of pixels in each blurring function. Using a 2-D polyphase decomposition of the image, we show that the obvious reformulation as an MIMO blind deconvolution problem fails unless the grid of downsampling is chosen carefully, in which case 2X2 downsampling can be achieved. We also show that irregular sampling allows reconstruction of an MXM high-resolution image from L2 low-resolution images blurred with an LXL blurring function can be achieved with as few as L2 + (M/L)2 pixels in each low-resolution image. Illustrative examples illustrate the points with explicit numbers.
The problem of kernel design for Cohen time-frequency distributions is formulated as a blind deconvolution problem. It is shown that the iterative blind deconvolution method (IBDM) used in image restoration problems can be successfully applied to solve the kernel design problem. We obtain the following results: (1) the rate of convergence depends on which domains the constraints are imposed (2) certain constraints are needed for algorithm convergence (3) the more constrained the kernel design is, the faster the rate of convergence (4) there are tradeoffs between constraints, e.g., compact support vs. satisfaction of marginals; (5) time-frequency distributions which are more amenable to visual interpretation can be obtained using this algorithm.