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NONLINEAR RECONSTRUCTION OF OVERSAMPLED COARSELY QUANTIZED SIGNALS
"... In the course of collecting real signals, one occasionally is faced with a coarsely quantized signal. In this paper the problem of reconstructing a coarsely quantized signal using a SavitskyGolay filter coupled with a nonlinearity is discussed. 1. ..."
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Cited by 2 (0 self)
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In the course of collecting real signals, one occasionally is faced with a coarsely quantized signal. In this paper the problem of reconstructing a coarsely quantized signal using a SavitskyGolay filter coupled with a nonlinearity is discussed. 1.
Coarsely Quantized Redundant Representations of Signals
, 2006
"... Digital data is the driving force behind much of our modern technology. The Internet and cellular phones are ubiquitous examples of the need to handle information accurately, efficiently, and robustly. The fact that digital signals and data sets can be processed with great precision and speed places ..."
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Digital data is the driving force behind much of our modern technology. The Internet and cellular phones are ubiquitous examples of the need to handle information accurately, efficiently, and robustly. The fact that digital signals and data sets can be processed with great precision and speed places high demands on providing accurate conversion between the analog and digital worlds. However, the technology used in the analog to digital (A/D) conversion by necessity involves analog devices which have physical limitations that, at first sight, conflict with these accuracy demands. For example, typical printers are only capable of applying a very limited set of ink tones (which may be as small as a single black tone) to paper for rendering intermediate grayscale levels. Similarly, in audio applications, the inaccuracy of analog circuits in working with binary expansions is a problem that routinely needs to be addressed. To cope with these problems, engineers have empirically developed special signal processing techniques leading to alternative signal and number representations that are quite different from the standard decimal or binary representations. Typical techniques take advantage of the fact that, although most analog devices used in A/D conversion fail to provide high precision in the amplitude domain, many of them are capable of sampling very densely in the time or the space domain over which the signals are defined. In these techniques, judiciously chosen dense arrangements of a limited set of discrete amplitude values are used to
Distributed Reception with CoarselyQuantized Observation Exchanges
"... Abstract—This paper considers the problem of jointly decoding binary phase shift keyed (BPSK) messages from a single distant transmitter to a cooperative receive cluster connected by a local area network (LAN). A distributed reception technique is proposed based on the exchange of coarselyquantize ..."
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Abstract—This paper considers the problem of jointly decoding binary phase shift keyed (BPSK) messages from a single distant transmitter to a cooperative receive cluster connected by a local area network (LAN). A distributed reception technique is proposed based on the exchange of coarselyquantized
Coarse Quantization with the Fast Digital Shearlet Transform
"... The fast digital shearlet transform (FDST) was recently introduced as a means to analyze natural images efficiently, owing to the fact that those are typically governed by cartoonlike structures. In this paper, we introduce and discuss a firstorder hybrid sigmadelta quantization algorithm for coa ..."
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for coarsely quantizing the shearlet coefficients generated by the FDST. Radial oversampling in the frequency domain together with our choice for the quantization helps suppress the reconstruction error in a similar way as firstorder sigmadelta quantization for finite frames. We provide a theoretical bound
COARSE QUANTIZATION FOR RANDOM INTERLEAVED SAMPLING OF BANDLIMITED SIGNALS
"... Abstract. The compatibility of unsynchronized interleaved uniform sampling with SigmaDelta analogtodigital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids {kT + Tn}k∈Z with offsets {Tn}Nn=1 ⊂ [0, T]. If the offsets Tn are chosen in ..."
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independently and uniformly at random from [0, T] and if the sample values of f are quantized with a first order SigmaDelta algorithm, then with high probability the quantization error f(t) − ef(t)  is at most of order N−1 logN. In memory of David Gottlieb–mentor and friend. 1.
Lower bounds for the error decay incurred by coarse quantization schemes
 Applied and Computational Harmonic Analysis
, 2012
"... Several analogtodigital conversion methods for bandlimited signals used in applications, such as Σ ∆ quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued from such methods measures the performance of a given scheme by t ..."
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Cited by 6 (4 self)
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Several analogtodigital conversion methods for bandlimited signals used in applications, such as Σ ∆ quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued from such methods measures the performance of a given scheme
1RootExponential Accuracy for Coarse Quantization of Finite Frame Expansions
"... In this note, we show that by quantizing the Ndimensional frame coefficients of signals in Rd using rthorder SigmaDelta quantization schemes, it is possible to achieve rootexponential accuracy in the oversampling rate λ: = N/d. In particular, we construct a family of finite frames tailored spec ..."
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specifically for coarse SigmaDelta quantization that admit themselves as both canonical duals and Sobolev duals. Our construction allows for error guarantees that behave as e−c λ, where under a mild restriction on the oversampling rate, the constants are absolute. Moreover, we show that harmonic frames can
Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding
 IEEE TRANS. ON INFORMATION THEORY
, 1999
"... We consider the problem of embedding one signal (e.g., a digital watermark), within another "host" signal to form a third, "composite" signal. The embedding is designed to achieve efficient tradeoffs among the three conflicting goals of maximizing informationembedding rate, mini ..."
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Cited by 495 (15 self)
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, minimizing distortion between the host signal and composite signal, and maximizing the robustness of the embedding. We introduce new classes of embedding methods, termed quantization index modulation (QIM) and distortioncompensated QIM (DCQIM), and develop convenient realizations in the form of what we
Determining Optical Flow
 ARTIFICIAL INTELLIGENCE
, 1981
"... Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent veloc ..."
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Cited by 2379 (9 self)
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velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely
SID 01 DIGEST 15.3: Color Error Diffusion: Accurate Luminance from Coarsely Quantized Displays
"... A video signal should use as many bits (gray levels) as possible, to obtain sufficient amplitude resolution for high quality images. However, (digital) displays use a limited number of bits. We propose a modification to the error diffusion algorithm that enables a decrease in the number of bits, wit ..."
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A video signal should use as many bits (gray levels) as possible, to obtain sufficient amplitude resolution for high quality images. However, (digital) displays use a limited number of bits. We propose a modification to the error diffusion algorithm that enables a decrease in the number of bits, without a decrease in luminance accuracy. 1
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