Concepts for on-board satellite image registration, volume 1

The NASA-NEEDS program goals present a requirement for on-board signal processing to achieve user-compatible, information-adaptive data acquisition. One very specific area of interest is the preprocessing required to register imaging sensor data which have been distorted by anomalies in subsatellite-point position and/or attitude control. The concepts and considerations involved in using state-of-the-art positioning systems such as the Global Positioning System (GPS) in concert with state-of-the-art attitude stabilization and/or determination systems to provide the required registration accuracy are discussed with emphasis on assessing the accuracy to which a given image picture element can be located and identified, determining those algorithms required to augment the registration procedure and evaluating the technology impact on performing these procedures on-board the satellite

Concepts for on-board satellite image registration. Volume 2: IAS prototype performance evaluation standard definition

Problems encountered in testing onboard signal processing hardware designed to achieve radiometric and geometric correction of satellite imaging data are considered. These include obtaining representative image and ancillary data for simulation and the transfer and storage of a large quantity of image data at very high speed. The high resolution, high speed preprocessing of LANDSAT-D imagery is considered

Generalizations of the sampling theorem: Seven decades after Nyquist

The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well-known form is Shannon's uniform-sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also well-known. The connection between such extensions and the theory of filter banks in DSP has been well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples. Applications in multiresolution computation and in digital spline interpolation are also reviewed

Self Super-Resolution for Magnetic Resonance Images using Deep Networks

High resolution magnetic resonance~(MR) imaging~(MRI) is desirable in many clinical applications, however, there is a trade-off between resolution, speed of acquisition, and noise. It is common for MR images to have worse through-plane resolution~(slice thickness) than in-plane resolution. In these MRI images, high frequency information in the through-plane direction is not acquired, and cannot be resolved through interpolation. To address this issue, super-resolution methods have been developed to enhance spatial resolution. As an ill-posed problem, state-of-the-art super-resolution methods rely on the presence of external/training atlases to learn the transform from low resolution~(LR) images to high resolution~(HR) images. For several reasons, such HR atlas images are often not available for MRI sequences. This paper presents a self super-resolution~(SSR) algorithm, which does not use any external atlas images, yet can still resolve HR images only reliant on the acquired LR image. We use a blurred version of the input image to create training data for a state-of-the-art super-resolution deep network. The trained network is applied to the original input image to estimate the HR image. Our SSR result shows a significant improvement on through-plane resolution compared to competing SSR methods.Comment: Accepted by IEEE International Symposium on Biomedical Imaging (ISBI) 201

Efficient Digital Pre-Filtering For Least-Squares Linear Approximation

In this paper we propose a very simple FIR pre-filter based method for near optimal least-squares linear approximation of discrete time signals. A digital pre-processing filter, which we demonstrate to be near-optimal, is applied to the signal before performing the usual linear interpolation. This leads to a non interpolating reconstruction of the signal, with good reconstruction quality and very limited computational cost. The basic formalism adopted to design the pre-filter has been derived from the framework introduced by Blu et Unser in [1]. To demonstrate the usability and the effectiveness of the approach, the proposed method has been applied to the problem of natural image resampling, which is typically applied when the image undergoes successive rotations. The performance obtained are very interesting, and the required computational effort is extremely low

Efficient digital pre-filtering for least squares linear approximation

In this paper we propose a very simple FIR pre-filter for near optimal least-squares linear approximation of discrete time signals. At first, a greedy least square approximation of the desired signal is derived using an efficient digital pre-processing filter, then the usual linear interpolation is applied to obtain the final result. This leads to a non interpolating reconstruction of the signal, with good reconstruction quality and very limited computational cost. The basic formalism adopted to design the pre-filter has been derived from the framework introduced by Blu et Unser. To demonstrate the usability and the effectiveness of the approach, the proposed method has been applied to the problem of natural image resampling, which is typically applied when the image undergoes successive rotations. The performance obtained are very interesting, and the required computational effort is extremely low

Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples

In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames. A seminal result of Beurling shows that sample points give rise to a classical Fourier frame provided they are relatively separated and of sufficient density. However, this result does not allow for arbitrary clustering of sample points, as is often the case in practice. Whilst keeping the density condition sharp and dimension independent, our first result removes the separation condition and shows that density alone suffices. However, this result does not lead to estimates for the frame bounds. A known result of Groechenig provides explicit estimates, but only subject to a density condition that deteriorates linearly with dimension. In our second result we improve these bounds by reducing the dimension dependence. In particular, we provide explicit frame bounds which are dimensionless for functions having compact support contained in a sphere. Next, we demonstrate how our two main results give new insight into a reconstruction algorithm---based on the existing generalized sampling framework---that allows for stable and quasi-optimal reconstruction in any particular basis from a finite collection of samples. Finally, we construct sufficiently dense sampling schemes that are often used in practice---jittered, radial and spiral sampling schemes---and provide several examples illustrating the effectiveness of our approach when tested on these schemes