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—One of the fundamental assumptions in traditional sampling theorems is that the signals to be sampled come from a single vector space (e.g., bandlimited functions). However, in many cases of practical interest the sampled signals actually live in a union of subspaces. Examples include piecewise polynomials, sparse representations, nonuniform splines,(More)
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed. Just as the classical result provides a tradeoff between signal localization in time and frequency, this result provides a(More)
In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of 2-D signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. We propose a new family of filter banks, named(More)
With the ever increasing computational power of modern day processors, it has become feasible to use more robust and computationally complex algorithms that increase the resolution of images without distorting edges and contours. We present a novel image interpolation algorithm that uses the new contourlet transform to improve the regularity of object(More)
We study a new image sensor that is reminiscent of a traditional photographic film. Each pixel in the sensor has a binary response, giving only a 1-bit quantized measurement of the local light intensity. To analyze its performance, we formulate the oversampled binary sensing scheme as a parameter estimation problem based on quantized Poisson statistics. We(More)
Recent advances in materials, devices and fabrication technologies have motivated a strong momentum in developing solid-state sensors that can detect individual photons in space and time. It has been envisioned that such sensors can eventually achieve very high spatial resolutions (e.g., 10 9 pixels/chip) as well as high frame rates (e.g., 10 6 frames/sec).(More)
Imagine that you are blindfolded inside an unknown room. You snap your fingers and listen to the room's response. Can you hear the shape of the room? Some people can do it naturally, but can we design computer algorithms that hear rooms? We show how to compute the shape of a convex polyhedral room from its response to a known sound, recorded by a few(More)
—In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from the magnitude of its Fourier transform to enable the reconstruction of the original signal. A fundamental question then(More)
We propose a randomized version of the nonlocal means (NLM) algorithm for large-scale image filtering. The new algorithm, called Monte Carlo nonlocal means (MCNLM), speeds up the classical NLM by computing a small subset of image patch distances, which are randomly selected according to a designed sampling pattern. We make two contributions. First, we(More)