Sub-Pixel Registration of Wavelet-Encoded Images

Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and non-destructive testing in manufacturing, to name a few. Recently, these technologies have been trending towards wavelet encoded imaging and sparse/compressive sensing. The former plays a crucial role in reducing imaging artifacts, while the latter significantly increases the acquisition speed. In view of these new emerging needs for applications of wavelet encoded imaging, we propose a sub-pixel registration method that can achieve direct wavelet domain registration from a sparse set of coefficients. We make the following contributions: (i) We devise a method of decoupling scale, rotation, and translation parameters in the Haar wavelet domain, (ii) We derive explicit mathematical expressions that define in-band sub-pixel registration in terms of wavelet coefficients, (iii) Using the derived expressions, we propose an approach to achieve in-band subpixel registration, avoiding back and forth transformations. (iv) Our solution remains highly accurate even when a sparse set of coefficients are used, which is due to localization of signals in a sparse set of wavelet coefficients. We demonstrate the accuracy of our method, and show that it outperforms the state-of-the-art on simulated and real data, even when the data is sparse

Non-Linear Phase-Shifting of Haar Wavelets for Run-Time All-Frequency Lighting

This paper focuses on real-time all-frequency image-based rendering using an innovative solution for run-time computation of light transport. The approach is based on new results derived for non-linear phase shifting in the Haar wavelet domain. Although image-based methods for real-time rendering of dynamic glossy objects have been proposed, they do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements and real-time rendering when both varying light and viewpoint changes are required together with high sampling rates for high frequency lighting of glossy material. On the other hand, current methods cannot handle object rotation, which is one of the paramount issues for all PRT methods using wavelets. This latter problem arises because the precomputed data are defined in a global coordinate system and encoded in the wavelet domain, while the object is rotated in a local coordinate system. At the root of all the above problems is the lack of efficient run-time solution to the nontrivial problem of rotating wavelets (a non-linear phase-shift), which we solve in this paper

Estimation of Physiological Motion Using Highly Accelerated Continuous 2D MRI

Patient motion is well-known for degrading image quality during medical imaging. Especially positron emission tomography (PET) is susceptible to motion due to its usually long scan times. In hybrid PET/MRI (magnetic resonance imaging), simultaneously acquired dynamic MRI data can be used to correct for motion. Usually, MRI model-based motion correction approaches are applied to the PET data. However, these approaches may fail for non-predictable, irregular motion. We propose a novel approach for the continuous and real-time tracking of motion using highly accelerated, dynamic MRI for an accurate motion estimation. For this purpose, a TurboFLASH sequence is utilized in single-shot mode with additional exploiting GRAPPA acceleration. Sampling frequency for one slice is up to 26 ms and 520 ms for one 3D volume of 20 coronal slices. Principal component analysis and a phase-sensitive resorting of slices is performed to restore temporal consistency of the volumes. Motion is estimated from these volumes using hyper-elastic registration. The approach is validated with the help of a dynamic thorax phantom as well as with eleven healthy volunteers. Phantom ground-truth data demonstrates that the approach produces an accurate motion estimation. Volunteer validation proves that the approach is also valid for different respiratory amplitudes including highly irregular breathing. The approach could be proved to be promising for a continuous PET motion correction

SPARCOM: Sparsity Based Super-Resolution Correlation Microscopy

In traditional optical imaging systems, the spatial resolution is limited by the physics of diffraction, which acts as a low-pass filter. The information on sub-wavelength features is carried by evanescent waves, never reaching the camera, thereby posing a hard limit on resolution: the so-called diffraction limit. Modern microscopic methods enable super-resolution, by employing florescence techniques. State-of-the-art localization based fluorescence subwavelength imaging techniques such as PALM and STORM achieve sub-diffraction spatial resolution of several tens of nano-meters. However, they require tens of thousands of exposures, which limits their temporal resolution. We have recently proposed SPARCOM (sparsity based super-resolution correlation microscopy), which exploits the sparse nature of the fluorophores distribution, alongside a statistical prior of uncorrelated emissions, and showed that SPARCOM achieves spatial resolution comparable to PALM/STORM, while capturing the data hundreds of times faster. Here, we provide a detailed mathematical formulation of SPARCOM, which in turn leads to an efficient numerical implementation, suitable for large-scale problems. We further extend our method to a general framework for sparsity based super-resolution imaging, in which sparsity can be assumed in other domains such as wavelet or discrete-cosine, leading to improved reconstructions in a variety of physical settings.Comment: 31 page

An Invariant Model of the Significance of Different Body Parts in Recognizing Different Actions

In this paper, we show that different body parts do not play equally important roles in recognizing a human action in video data. We investigate to what extent a body part plays a role in recognition of different actions and hence propose a generic method of assigning weights to different body points. The approach is inspired by the strong evidence in the applied perception community that humans perform recognition in a foveated manner, that is they recognize events or objects by only focusing on visually significant aspects. An important contribution of our method is that the computation of the weights assigned to body parts is invariant to viewing directions and camera parameters in the input data. We have performed extensive experiments to validate the proposed approach and demonstrate its significance. In particular, results show that considerable improvement in performance is gained by taking into account the relative importance of different body parts as defined by our approach.Comment: arXiv admin note: substantial text overlap with arXiv:1705.04641, arXiv:1705.05741, arXiv:1705.0443

A Unified Framework for Multi-Sensor HDR Video Reconstruction

One of the most successful approaches to modern high quality HDR-video capture is to use camera setups with multiple sensors imaging the scene through a common optical system. However, such systems pose several challenges for HDR reconstruction algorithms. Previous reconstruction techniques have considered debayering, denoising, resampling (align- ment) and exposure fusion as separate problems. In contrast, in this paper we present a unifying approach, performing HDR assembly directly from raw sensor data. Our framework includes a camera noise model adapted to HDR video and an algorithm for spatially adaptive HDR reconstruction based on fitting of local polynomial approximations to observed sensor data. The method is easy to implement and allows reconstruction to an arbitrary resolution and output mapping. We present an implementation in CUDA and show real-time performance for an experimental 4 Mpixel multi-sensor HDR video system. We further show that our algorithm has clear advantages over existing methods, both in terms of flexibility and reconstruction quality

Volumetric Super-Resolution of Multispectral Data

Most multispectral remote sensors (e.g. QuickBird, IKONOS, and Landsat 7 ETM+) provide low-spatial high-spectral resolution multispectral (MS) or high-spatial low-spectral resolution panchromatic (PAN) images, separately. In order to reconstruct a high-spatial/high-spectral resolution multispectral image volume, either the information in MS and PAN images are fused (i.e. pansharpening) or super-resolution reconstruction (SRR) is used with only MS images captured on different dates. Existing methods do not utilize temporal information of MS and high spatial resolution of PAN images together to improve the resolution. In this paper, we propose a multiframe SRR algorithm using pansharpened MS images, taking advantage of both temporal and spatial information available in multispectral imagery, in order to exceed spatial resolution of given PAN images. We first apply pansharpening to a set of multispectral images and their corresponding PAN images captured on different dates. Then, we use the pansharpened multispectral images as input to the proposed wavelet-based multiframe SRR method to yield full volumetric SRR. The proposed SRR method is obtained by deriving the subband relations between multitemporal MS volumes. We demonstrate the results on Landsat 7 ETM+ images comparing our method to conventional techniques.Comment: arXiv admin note: text overlap with arXiv:1705.0125

A high-order wideband direct solver for electromagnetic scattering from bodies of revolution

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as $\omega \to 0$ in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nystr\"om discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples

Splines are Universal Solutions of Linear Inverse Problems with Generalized-TV regularization

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by considering more general operators than the derivative. This leads us to the definition of the generalized Beppo-Levi space M, which is further identified as the direct sum of two Banach spaces. We then prove that the minimization of the generalized total variation (gTV) over M, subject to some arbitrary (convex) consistency constraints on the linear measurements of the signal, admits nonuniform L-spline solutions with fewer knots than the number of measurements. This shows that non-uniform splines are universal solutions of continuous-domain linear inverse problems with LASSO, L1, or TV-like regularization constraints. Remarkably, the spline-type is fully determined by the choice of L and does not depend on the actual nature of the measurements.Comment: 28 pages, 1 figur

Single Image Action Recognition by Predicting Space-Time Saliency

We propose a novel approach based on deep Convolutional Neural Networks (CNN) to recognize human actions in still images by predicting the future motion, and detecting the shape and location of the salient parts of the image. We make the following major contributions to this important area of research: (i) We use the predicted future motion in the static image (Walker et al., 2015) as a means of compensating for the missing temporal information, while using the saliency map to represent the the spatial information in the form of location and shape of what is predicted as significant. (ii) We cast action classification in static images as a domain adaptation problem by transfer learning. We first map the input static image to a new domain that we refer to as the Predicted Optical Flow-Saliency Map domain (POF-SM), and then fine-tune the layers of a deep CNN model trained on classifying the ImageNet dataset to perform action classification in the POF-SM domain. (iii) We tested our method on the popular Willow dataset. But unlike existing methods, we also tested on a more realistic and challenging dataset of over 2M still images that we collected and labeled by taking random frames from the UCF-101 video dataset. We call our dataset the UCF Still Image dataset or UCFSI-101 in short. Our results outperform the state of the art