The human visual system appears to be capable of temporally integrating information in a video sequence in such a way that the perceived spatial resolution of a sequence appears much higher than the spatial resolution of an individual frame. While the mechanisms in the human visual system which do this are unknown, the effect is not too surprising given that temporally adjacent frames in a video sequence contain slightly different, but unique, information. This paper addresses how to utilize both the spatial and temporal information present in a short image sequence to create a single high-resolution video frame. A novel observation model based on motion compensated subsampling is proposed for a video sequence. Since the reconstruction problem is ill-posed, Bayesian restoration with a discontinuity-preserving prior image model is used to extract a high-resolution video still given a short low-resolution sequence. Estimates computed from a low-resolution image sequence containing a subp...

Abstract 1 Over the past ten years there has been considerable interest in statistically optimal reconstruction of image cross-sections from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. In this paper we propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We show that the ICD iterations require approximately the same amount of computation per iteration as EM based approaches, but the new method converges much more rapidly (in our experiments typically 5 iterations). Other advantages of the ICD method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are simply incorporated.

Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for data-driven and flow-driven, isotropic and anisotropic, as well as spatial and spatio-temporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are well-posed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flow-driven regularizers is identified, and a design criterion is proposed for constructing anisotropic flow-driven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.

This article deals with the problem of restoring and motion segmenting noisy image sequences with a static background. Usually, motion segmentation and image restoration are considered separately in image sequence restoration. Moreover, motion segmentation is often noise sensitive. In this article, the motion segmentation and the image restoration parts are performed in a coupled way, allowing the motion segmentation part to positively influence the restoration part and vice-versa. This is the key of our approach that allows to deal simultaneously with the problem of restoration and motion segmentation. To this end, we propose a theoretically justified optimization problem that permits to take into account both requirements. The model is theoretically justified. Existence and unicity are proved in the space of bounded variations. A suitable numerical scheme based on half quadratic minimization is then proposed and its convergence and stability demonstrated. Experimental results obtaine...

Abstract—There are a number of useful methods for creating high-quality video or still images from a lower quality video source. The best of these involve motion compensating a number of video frames to produce the desired video or still. These methods are formulated in the space domain and they require that the input be expressed in that format. More and more frequently, however, video sources are presented in a compressed format, such as MPEG, H.263, or DV. Ironically, there is important information in the compressed domain representation that is lost if the video is first decompressed and then used with a spatial-domain method. In particular, quantization information is lost once the video has been decompressed. Here, we propose a motion-compensated, transform-domain super-resolution procedure for creating high-quality video or still images that directly incorporates the transform-domain quantization information by working with the compressed bit stream. We apply this new formulation to MPEG-compressed video and demonstrate its effectiveness. Index Terms—Constrained optimization, image reconstruction, MAP, POCS, resolution enhancement, super-resolution, transform-domain restoration, video quality.

This paper deals with establishing relations between a number of widely-used nonlinear filters for digital image processing. We cover robust statistical estimation with (local) M-estimators, local mode filtering in image or histogram space, bilateral filtering, nonlinear diffusion, and regularisation approaches. Although these methods originate in different mathematical theories, we show that their implementation reveals a highly similar structure. We demonstrate that all these methods can be cast into a unified framework of functional minimisation combining nonlocal data and nonlocal smoothness terms. This unification contributes to a better understanding of the individual methods, and it opens the way to new techniques combining the advantages of known filters. Keywords: image analysis, M-estimators, mode filtering, nonlinear diffusion, bilateral filter, regularisation

When transmitting compressed video over a data network, one has to deal with how channel errors affect the decoding process. This is particularly problematic with data loss or erasures. In this paper we describe techniques to address this problem in the context of networks where channel errors or congestion can result in the loss of entire macroblocks when MPEG video is transmitted. We describe spatial and temporal techniques for the recovery of lost macroblocks. In particular, we develop estimation techniques for the reconstruction of missing macroblocks using a Markov Random Field model. We show that the widely used heuristic motion compensated error concealment technique based on averaging motion vectors is a special case of our estimation technique. We further describe a technique that can be implemented in real-time.

Abstract—When transmitting compressed video over a data network, one has to deal with how channel errors affect the decoding process. This is particularly a problem with data loss or erasures. In this paper we describe techniques to address this problem in the context of Asynchronous Transfer Mode (ATM) networks. Our techniques can be extended to other types of data networks such as wireless networks. In ATM networks channel errors or congestion cause data to be dropped, which results in the loss of entire macroblocks when MPEG video is transmitted. In order to reconstruct the missing data, the location of these macroblocks must be known. We describe a technique for packing ATM cells with compressed data, whereby the location of missing macroblocks in the encoded video stream can be found. This technique also permits the proper decoding of correctly received macroblocks, and thus prevents the loss of ATM cells from affecting the decoding process. The packing strategy can also be used for wireless or other types of data networks. We also describe spatial and temporal techniques for the recovery of lost macroblocks. In particular, we develop several optimal estimation techniques for the reconstruction of missing macroblocks that contain both spatial and temporal information using a Markov random field model. We further describe a sub-optimal estimation technique that can be implemented in real time. Index Terms—ATM, cell loss, cell packing, error concealment, motion vectors, Markov random field, spatial reconstruction, temporal reconstruction. I.

In this paper we propose a new way to iteratively solve the image reconstruction problem from noisy images or noisy data linearly related to the pixel intensities. This is done by exploiting the relation between Tikhonov regularization and multiobjective optimization to obtain iteratively approximations to the Tikhonov L-curve and its corner. Monitoring the change of the approximate L-curves allows us to adjust the regularization parameter adaptively during a preconditioned conjugate gradient iteration, so that the desired image can be reconstructed with a low number of iterations. Nonnegativity constraints are taken into account automatically. We present test results on image reconstruction in positron emission tomography (PET). Keywords: Tikhonov regularization, multiobjective optimization, ill-posed, L-curve, envelope, preconditioned conjugate gradients, image reconstruction, positron emission tomography (PET) 1991 MSC Classification: primary 65F10, secondary 65R30, 68U10, 90C29, 9...

Abstract—Hyperspectral images are used for aerial and space imagery applications, including target detection, tracking, agricultural, and natural resource exploration. Unfortunately, atmospheric scattering, secondary illumination, changing viewing angles, and sensor noise degrade the quality of these images. Improving their resolution has a high payoff, but applying superresolution techniques separately to every spectral band is problematic for two main reasons. First, the number of spectral bands can be in the hundreds, which increases the computational load excessively. Second, considering the bands separately does not make use of the information that is present across them. Furthermore, separate band super resolution does not make use of the inherent low dimensionality of the spectral data, which can effectively be used to improve the robustness against noise. In this paper, we introduce a novel super-resolution method for hyperspectral images. An integral part of our work is to model the hyperspectral image acquisition process. We propose a model that enables us to represent the hyperspectral observations from different wavelengths as weighted linear combinations of a small number of basis image planes. Then, a method for applying super resolution to hyperspectral images using this model is presented. The method fuses information from multiple observations and spectral bands to improve spatial resolution and reconstruct the spectrum of the observed scene as a combination of a small number of spectral basis functions. Index Terms—Hyperspectral, image reconstruction, information fusion, resolution enhancement, spectral, super resolution.