Abstract-Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials.Even though these signals are not bandlimited, we show that they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case. In particular, we show how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinite-length signals with finite local rate of innovation, we show local sampling and reconstruction based on spline kernels.The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and error-correction coding. This leads to standard computational procedures for solving the sampling problem, which we show through experimental results.Applications of these new sampling results can be found in signal processing, communications systems, and biological systems.

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In this paper, we present a no-reference blur metric for images and video. The blur metric is based on the analysis of the spread of the edges in an image. Its perceptual significance is validated through subjective experiments. The novel metric is near real-time, has low computational complexity and is shown to perform well over a range of image content. Potential applications include optimization of source coding, network resource management and autofocus of an image capturing device.

We present a full-and no-reference blur metric as well as a full-reference ringing metric. These metrics are based on an analysis of the edges and adjacent regions in an image and have very low computational complexity. As blur and ringing are typical artifacts of wavelet compression, the metrics are then applied to JPEG2000 coded images. Their perceptual significance is corroborated through a number of subjective experiments. The results show that the proposed metrics perform well over a wide range of image content and distortion levels. Potential applications include source coding optimization and network resource management.

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