4,411 research outputs found
Weighted universal image compression
We describe a general coding strategy leading to a family of universal image compression systems designed to give good performance in applications where the statistics of the source to be compressed are not available at design time or vary over time or space. The basic approach considered uses a two-stage structure in which the single source code of traditional image compression systems is replaced with a family of codes designed to cover a large class of possible sources. To illustrate this approach, we consider the optimal design and use of two-stage codes containing collections of vector quantizers (weighted universal vector quantization), bit allocations for JPEG-style coding (weighted universal bit allocation), and transform codes (weighted universal transform coding). Further, we demonstrate the benefits to be gained from the inclusion of perceptual distortion measures and optimal parsing. The strategy yields two-stage codes that significantly outperform their single-stage predecessors. On a sequence of medical images, weighted universal vector quantization outperforms entropy coded vector quantization by over 9 dB. On the same data sequence, weighted universal bit allocation outperforms a JPEG-style code by over 2.5 dB. On a collection of mixed test and image data, weighted universal transform coding outperforms a single, data-optimized transform code (which gives performance almost identical to that of JPEG) by over 6 dB
Quantum Hopfield neural network
Quantum computing allows for the potential of significant advancements in
both the speed and the capacity of widely used machine learning techniques.
Here we employ quantum algorithms for the Hopfield network, which can be used
for pattern recognition, reconstruction, and optimization as a realization of a
content-addressable memory system. We show that an exponentially large network
can be stored in a polynomial number of quantum bits by encoding the network
into the amplitudes of quantum states. By introducing a classical technique for
operating the Hopfield network, we can leverage quantum algorithms to obtain a
quantum computational complexity that is logarithmic in the dimension of the
data. We also present an application of our method as a genetic sequence
recognizer.Comment: 13 pages, 3 figures, final versio
Sensor encoding using lateral inhibited, self-organized cellular neural networks
The paper focuses on the division of the sensor field into subsets of sensor events and proposes the linear transformation with the smallest achievable error for reproduction: the transform coding approach using the principal component analysis (PCA). For the implementation of the PCA, this paper introduces a new symmetrical, lateral inhibited neural network model, proposes an objective function for it and deduces the corresponding learning rules. The necessary conditions for the learning rate and the inhibition parameter for balancing the crosscorrelations vs. the autocorrelations are computed. The simulation reveals that an increasing inhibition can speed up the convergence process in the beginning slightly. In the remaining paper, the application of the network in picture encoding is discussed. Here, the use of non-completely connected networks for the self-organized formation of templates in cellular neural networks is shown. It turns out that the self-organizing Kohonen map is just the non-linear, first order approximation of a general self-organizing scheme. Hereby, the classical transform picture coding is changed to a parallel, local model of linear transformation by locally changing sets of self-organized eigenvector projections with overlapping input receptive fields. This approach favors an effective, cheap implementation of sensor encoding directly on the sensor chip. Keywords: Transform coding, Principal component analysis, Lateral inhibited network, Cellular neural network, Kohonen map, Self-organized eigenvector jets
Optimising Spatial and Tonal Data for PDE-based Inpainting
Some recent methods for lossy signal and image compression store only a few
selected pixels and fill in the missing structures by inpainting with a partial
differential equation (PDE). Suitable operators include the Laplacian, the
biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The
quality of such approaches depends substantially on the selection of the data
that is kept. Optimising this data in the domain and codomain gives rise to
challenging mathematical problems that shall be addressed in our work.
In the 1D case, we prove results that provide insights into the difficulty of
this problem, and we give evidence that a splitting into spatial and tonal
(i.e. function value) optimisation does hardly deteriorate the results. In the
2D setting, we present generic algorithms that achieve a high reconstruction
quality even if the specified data is very sparse. To optimise the spatial
data, we use a probabilistic sparsification, followed by a nonlocal pixel
exchange that avoids getting trapped in bad local optima. After this spatial
optimisation we perform a tonal optimisation that modifies the function values
in order to reduce the global reconstruction error. For homogeneous diffusion
inpainting, this comes down to a least squares problem for which we prove that
it has a unique solution. We demonstrate that it can be found efficiently with
a gradient descent approach that is accelerated with fast explicit diffusion
(FED) cycles. Our framework allows to specify the desired density of the
inpainting mask a priori. Moreover, is more generic than other data
optimisation approaches for the sparse inpainting problem, since it can also be
extended to nonlinear inpainting operators such as EED. This is exploited to
achieve reconstructions with state-of-the-art quality.
We also give an extensive literature survey on PDE-based image compression
methods
Online Multi-Stage Deep Architectures for Feature Extraction and Object Recognition
Multi-stage visual architectures have recently found success in achieving high classification accuracies over image datasets with large variations in pose, lighting, and scale. Inspired by techniques currently at the forefront of deep learning, such architectures are typically composed of one or more layers of preprocessing, feature encoding, and pooling to extract features from raw images. Training these components traditionally relies on large sets of patches that are extracted from a potentially large image dataset. In this context, high-dimensional feature space representations are often helpful for obtaining the best classification performances and providing a higher degree of invariance to object transformations. Large datasets with high-dimensional features complicate the implementation of visual architectures in memory constrained environments. This dissertation constructs online learning replacements for the components within a multi-stage architecture and demonstrates that the proposed replacements (namely fuzzy competitive clustering, an incremental covariance estimator, and multi-layer neural network) can offer performance competitive with their offline batch counterparts while providing a reduced memory footprint. The online nature of this solution allows for the development of a method for adjusting parameters within the architecture via stochastic gradient descent. Testing over multiple datasets shows the potential benefits of this methodology when appropriate priors on the initial parameters are unknown. Alternatives to batch based decompositions for a whitening preprocessing stage which take advantage of natural image statistics and allow simple dictionary learners to work well in the problem domain are also explored. Expansions of the architecture using additional pooling statistics and multiple layers are presented and indicate that larger codebook sizes are not the only step forward to higher classification accuracies. Experimental results from these expansions further indicate the important role of sparsity and appropriate encodings within multi-stage visual feature extraction architectures
The Complexity of Relating Quantum Channels to Master Equations
Completely positive, trace preserving (CPT) maps and Lindblad master
equations are both widely used to describe the dynamics of open quantum
systems. The connection between these two descriptions is a classic topic in
mathematical physics. One direction was solved by the now famous result due to
Lindblad, Kossakowski Gorini and Sudarshan, who gave a complete
characterisation of the master equations that generate completely positive
semi-groups. However, the other direction has remained open: given a CPT map,
is there a Lindblad master equation that generates it (and if so, can we find
it's form)? This is sometimes known as the Markovianity problem. Physically, it
is asking how one can deduce underlying physical processes from experimental
observations.
We give a complexity theoretic answer to this problem: it is NP-hard. We also
give an explicit algorithm that reduces the problem to integer semi-definite
programming, a well-known NP problem. Together, these results imply that
resolving the question of which CPT maps can be generated by master equations
is tantamount to solving P=NP: any efficiently computable criterion for
Markovianity would imply P=NP; whereas a proof that P=NP would imply that our
algorithm already gives an efficiently computable criterion. Thus, unless P
does equal NP, there cannot exist any simple criterion for determining when a
CPT map has a master equation description.
However, we also show that if the system dimension is fixed (relevant for
current quantum process tomography experiments), then our algorithm scales
efficiently in the required precision, allowing an underlying Lindblad master
equation to be determined efficiently from even a single snapshot in this case.
Our work also leads to similar complexity-theoretic answers to a related
long-standing open problem in probability theory.Comment: V1: 43 pages, single column, 8 figures. V2: titled changed; added
proof-overview and accompanying figure; 50 pages, single column, 9 figure
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