| Abstract: |
We develop an approach for increasing the temporal resolution of a temporally blurred sequence of observations. Super-resolution is performed in time using a variational approach. By temporal super-resolution, we mean recovering rapidly evolving events that were corrupted by the induced blur of the sensor. A blurred sequence of observations is assumed to have been generated by convolution of a physical scene with a temporal rectangular convolution kernel whose support is the sensor exposure time. We solve the deconvolution problem using the Split-Bregman method. Such methodology is based on current research in sparse optimization and compressed sensing, which lead to unprecedented efficiencies for solving image reconstruction problems. We test our method using a simulated temporally blurred and noisy temporal precipitation sequence and show that our method significantly reduces the errors in the corrupted sequence.
A sensor has temporal resolution limited by the frame-rate and by the exposure time of the sensor. The sensor collects the information from the scene during the exposure time in order to generate each frame. As a consequence, the evolving scene is blurred, resulting in a distorted observation. The faster the scene evolves, the stronger the blur is. Such blur is therefore a temporal artifact. It is caused by temporal blurring, and not by spatial blurring, and should therefore be handled temporally. All pixels in the evolving scene are affected by the same temporal blur, which is a convolution with a temporal rectangular function. However, the temporal blur can only be observed in parts of the image that have undergone temporal changes. Temporal blurring is particularly pronounced for geostationary-satellite microwave sensors such as the proposed Geostationary Synthetic Thinned Aperture Radiometer (GeoSTAR), where the exposure time may be 15 minutes or more. This is generally adequate for observation of storms and other dynamic atmospheric phenomena that evolve on time scales of 30-60 minutes or longer, but some phenomena such as intense convective rain can evolve much more rapidly. GeoSTAR is heavily oversampled in time – each exposure interval is aggregated from a continuous stream of 1-minute subsamples – and it therefore lends itself well to super-resolution.
Temporal super-resolution methods were previously proposed. However, these methods rely on objects of interest being tracked through the sequence using region based matching. They also require the estimation of objects' motions. In our previous work on temporal resolution enhancement, we considered the evolving sequence of observations to be embedded in a deformable medium, and enhanced temporal resolution of a sequence using nonlinear viscous fluid registration model. Given a pair of spatially resolved frames, we solved an image registration problem in order to find an unknown intermediate frame. In this paper, we solve a different temporal super-resolution problem. We recover rapidly evolving events that were blurred temporally by the convolution with a temporal rectangular function.
Our approach is based on our previous work on spatial super-resolution, where we formally solved the deconvolution inverse problem for images corrupted by spatial blur. Since the convolution problem is highly ill-posed, regularization was applied to achieve stability while preserving a priori properties of the solution. We formulated the restoration problem within the variational framework, using the total variation (TV) regularization. The minimization of the TV norm does not penalize edges in an image. We performed the total variation based deconvolution within the Split Bregman optimization framework to achieve a significant computational time improvement over already robust total-variation gradient descent based techniques. In this paper, we generalize an efficient TV-based Split Bregman deconvolution method to efficiently reconstruct temporally blurred and noisy sequences of observations.
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