These notes stem from lectures given by the first author (JM) at the 2008 Moonshine Conference in Kashiwa and contain a number of new perspectives and observations on Monstrous Moonshine. Because many new points have not appeared anywhere in print, i
t is thought expedient to update, annotate and clarify them (as footnotes), an editorial task which the second author (YHH) is more than delighted to undertake. We hope the various puzzles and correspondences, delivered in a personal and casual manner, will serve as
Fourier domain methods are fast algorithms for SAR imaging. They typically involve an interpolation in the frequency domain to re-grid non-uniform data so inverse fast Fourier transforms can be performed. In this paper, we apply a frame reconstructio
n algorithm, extending the non-uniform fast Fourier transform, to stripmap SAR data. Further, we present an improved thresholded frame reconstruction algorithm for robust performance and improved computational efficiency. We demonstrate compelling results on real stripmap SAR data.
Acquisition of Synthetic Aperture Sonar (SAS) datasets is bottlenecked by the costly deployment of SAS imaging systems, and even when data acquisition is possible,the data is often skewed towards containing barren seafloor rather than objects of inte
rest. We present a novel pipeline, called SAS GAN, which couples an optical renderer with a generative adversarial network (GAN) to synthesize realistic SAS images of targets on the seafloor. This coupling enables high levels of SAS image realism while enabling control over image geometry and parameters. We demonstrate qualitative results by presenting examples of images created with our pipeline. We also present quantitative results through the use of t-SNE and the Frechet Inception Distance to argue that our generated SAS imagery potentially augments SAS datasets more effectively than an off-the-shelf GAN.
We study general properties of the dessins denfants associated with the Hecke congruence subgroups $Gamma_0(N)$ of the modular group $mathrm{PSL}_2(mathbb{R})$. The definition of the $Gamma_0(N)$ as the stabilisers of couples of projective lattices i
n a two-dimensional vector space gives an interpretation of the quotient set $Gamma_0(N)backslashmathrm{PSL}_2(mathbb{R})$ as the projective lattices $N$-hyperdistant from a reference one, and hence as the projective line over the ring $mathbb{Z}/Nmathbb{Z}$. The natural action of $mathrm{PSL}_2(mathbb{R})$ on the lattices defines a dessin denfant structure, allowing for a combinatorial approach to features of the classical modular curves, such as the torsion points and the cusps. We tabulate the dessins denfants associated with the $15$ Hecke congruence subgroups of genus zero, which arise in Moonshine for the Monster sporadic group.
There are many real-world classification problems wherein the issue of data imbalance (the case when a data set contains substantially more samples for one/many classes than the rest) is unavoidable. While under-sampling the problematic classes is a
common solution, this is not a compelling option when the large data class is itself diverse and/or the limited data class is especially small. We suggest a strategy based on recent work concerning limited data problems which utilizes a supplemental set of images with similar properties to the limited data class to aid in the training of a neural network. We show results for our model against other typical methods on a real-world synthetic aperture sonar data set. Code can be found at github.com/JohnMcKay/dataImbalance.
Any image recovery algorithm attempts to achieve the highest quality reconstruction in a timely manner. The former can be achieved in several ways, among which are by incorporating Bayesian priors that exploit natural image tendencies to cue in on re
levant phenomena. The Hierarchical Bayesian MAP (HB-MAP) is one such approach which is known to produce compelling results albeit at a substantial computational cost. We look to provide further analysis and insights into what makes the HB-MAP work. While retaining the proficient nature of HB-MAPs Type-I estimation, we propose a stochastic approximation-based approach to Type-II estimation. The resulting algorithm, fast stochastic HB-MAP (fsHBMAP), takes dramatically fewer operations while retaining high reconstruction quality. We employ our fsHBMAP scheme towards the problem of tomographic imaging and demonstrate that fsHBMAP furnishes promising results when compared to many competing methods.
Finding mines in Sonar imagery is a significant problem with a great deal of relevance for seafaring military and commercial endeavors. Unfortunately, the lack of enormous Sonar image data sets has prevented automatic target recognition (ATR) algorit
hms from some of the same advances seen in other computer vision fields. Namely, the boom in convolutional neural nets (CNNs) which have been able to achieve incredible results - even surpassing human actors - has not been an easily feasible route for many practitioners of Sonar ATR. We demonstrate the power of one avenue to incorporating CNNs into Sonar ATR: transfer learning. We first show how well a straightforward, flexible CNN feature-extraction strategy can be used to obtain impressive if not state-of-the-art results. Secondly, we propose a way to utilize the powerful transfer learning approach towards multiple instance target detection and identification within a provided synthetic aperture Sonar data set.
Sonar imaging has seen vast improvements over the last few decades due in part to advances in synthetic aperture Sonar (SAS). Sophisticated classification techniques can now be used in Sonar automatic target recognition (ATR) to locate mines and othe
r threatening objects. Among the most promising of these methods is sparse reconstruction-based classification (SRC) which has shown an impressive resiliency to noise, blur, and occlusion. We present a coherent strategy for expanding upon SRC for Sonar ATR that retains SRCs robustness while also being able to handle targets with diverse geometric arrangements, bothersome Rayleigh noise, and unavoidable background clutter. Our method, pose corrected sparsity (PCS), incorporates a novel interpretation of a spike and slab probability distribution towards use as a Bayesian prior for class-specific discrimination in combination with a dictionary learning scheme for localized patch extractions. Additionally, PCS offers the potential for anomaly detection in order to avoid false identifications of tested objects from outside the training set with no additional training required. Compelling results are shown using a database provided by the United States Naval Surface Warfare Center.
Recent progress in synthetic aperture sonar (SAS) technology and processing has led to significant advances in underwater imaging, outperforming previously common approaches in both accuracy and efficiency. There are, however, inherent limitations to
current SAS reconstruction methodology. In particular, popular and efficient Fourier domain SAS methods require a 2D interpolation which is often ill conditioned and inaccurate, inevitably reducing robustness with regard to speckle and inaccurate sound-speed estimation. To overcome these issues, we propose using the frame theoretic convolution gridding (FTCG) algorithm to handle the non-uniform Fourier data. FTCG extends upon non-uniform fast Fourier transform (NUFFT) algorithms by casting the NUFFT as an approximation problem given Fourier frame data. The FTCG has been show to yield improved accuracy at little more computational cost. Using simulated data, we outline how the FTCG can be used to enhance current SAS processing.
We describe examples motivated by the work of Serre and Abhyankar.
