Distributed Functional Scalar Quantization Simplified

Distributed functional scalar quantization (DFSQ) theory provides optimality conditions and predicts performance of data acquisition systems in which a computation on acquired data is desired. We address two limitations of previous works: prohibitively expensive decoder design and a restriction to sources with bounded distributions. We rigorously show that a much simpler decoder has equivalent asymptotic performance as the conditional expectation estimator previously explored, thus reducing decoder design complexity. The simpler decoder has the feature of decoupled communication and computation blocks. Moreover, we extend the DFSQ framework with the simpler decoder to acquire sources with infinite-support distributions such as Gaussian or exponential distributions. Finally, through simulation results we demonstrate that performance at moderate coding rates is well predicted by the asymptotic analysis, and we give new insight on the rate of convergence

Neural scaling laws for an uncertain world

Autonomous neural systems must efficiently process information in a wide range of novel environments, which may have very different statistical properties. We consider the problem of how to optimally distribute receptors along a one-dimensional continuum consistent with the following design principles. First, neural representations of the world should obey a neural uncertainty principle---making as few assumptions as possible about the statistical structure of the world. Second, neural representations should convey, as much as possible, equivalent information about environments with different statistics. The results of these arguments resemble the structure of the visual system and provide a natural explanation of the behavioral Weber-Fechner law, a foundational result in psychology. Because the derivation is extremely general, this suggests that similar scaling relationships should be observed not only in sensory continua, but also in neural representations of ``cognitive' one-dimensional quantities such as time or numerosity

2-step scalar deadzone quantization for bitplane image coding

Modern lossy image coding systems generate a quality progressive codestream that, truncated at increasing rates, produces an image with decreasing distortion. Quality progressivity is commonly provided by an embedded quantizer that employs uniform scalar deadzone quantization (USDQ) together with a bitplane coding strategy. This paper introduces a 2-step scalar deadzone quantization (2SDQ) scheme that achieves same coding performance as that of USDQ while reducing the coding passes and the emitted symbols of the bitplane coding engine. This serves to reduce the computational costs of the codec and/or to code high dynamic range images. The main insights behind 2SDQ are the use of two quantization step sizes that approximate wavelet coefficients with more or less precision depending on their density, and a rate-distortion optimization technique that adjusts the distortion decreases produced when coding 2SDQ indexes. The integration of 2SDQ in current codecs is straightforward. The applicability and efficiency of 2SDQ are demonstrated within the framework of JPEG2000

Analysis-driven lossy compression of DNA microarray images

DNA microarrays are one of the fastest-growing new technologies in the field of genetic research, and DNA microarray images continue to grow in number and size. Since analysis techniques are under active and ongoing development, storage, transmission and sharing of DNA microarray images need be addressed, with compression playing a significant role. However, existing lossless coding algorithms yield only limited compression performance (compression ratios below 2:1), whereas lossy coding methods may introduce unacceptable distortions in the analysis process. This work introduces a novel Relative Quantizer (RQ), which employs non-uniform quantization intervals designed for improved compression while bounding the impact on the DNA microarray analysis. This quantizer constrains the maximum relative error introduced into quantized imagery, devoting higher precision to pixels critical to the analysis process. For suitable parameter choices, the resulting variations in the DNA microarray analysis are less than half of those inherent to the experimental variability. Experimental results reveal that appropriate analysis can still be performed for average compression ratios exceeding 4.5:1

Quantization in acquisition and computation networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 151-165).In modern systems, it is often desirable to extract relevant information from large amounts of data collected at different spatial locations. Applications include sensor networks, wearable health-monitoring devices and a variety of other systems for inference. Several existing source coding techniques, such as Slepian-Wolf and Wyner-Ziv coding, achieve asymptotic compression optimality in distributed systems. However, these techniques are rarely used in sensor networks because of decoding complexity and prohibitively long code length. Moreover, the fundamental limits that arise from existing techniques are intractable to describe for a complicated network topology or when the objective of the system is to perform some computation on the data rather than to reproduce the data. This thesis bridges the technological gap between the needs of real-world systems and the optimistic bounds derived from asymptotic analysis. Specifically, we characterize fundamental trade-offs when the desired computation is incorporated into the compression design and the code length is one. To obtain both performance guarantees and achievable schemes, we use high-resolution quantization theory, which is complementary to the Shannon-theoretic analyses previously used to study distributed systems. We account for varied network topologies, such as those where sensors are allowed to collaborate or the communication links are heterogeneous. In these settings, a small amount of intersensor communication can provide a significant improvement in compression performance. As a result, this work suggests new compression principles and network design for modern distributed systems. Although the ideas in the thesis are motivated by current and future sensor network implementations, the framework applies to a wide range of signal processing questions. We draw connections between the fidelity criteria studied in the thesis and distortion measures used in perceptual coding. As a consequence, we determine the optimal quantizer for expected relative error (ERE), a measure that is widely useful but is often neglected in the source coding community. We further demonstrate that applying the ERE criterion to psychophysical models can explain the Weber-Fechner law, a longstanding hypothesis of how humans perceive the external world. Our results are consistent with the hypothesis that human perception is Bayesian optimal for information acquisition conditioned on limited cognitive resources, thereby supporting the notion that the brain is efficient at acquisition and adaptation.by John Z. Sun.Ph.D

Scalar Quantization for Relative Error

Quantizers for probabilistic sources are usually optimized for mean-squared error. In many applications, maintaining low relative error is a more suitable objective. This measure has previously been heuristically connected with the use of logarithmic companding in perceptual coding. We derive optimal companding quantizers for fixed rate and variable rate under high-resolution assumptions. The analysis shows logarithmic companding is optimal for variable-rate quantization but generally not for fixed-rate quantization. Naturally, the improvement in relative error from using a correctly optimized quantizer can be arbitrarily large. We extend this framework for a large class of nondifference distortions