Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D\leq \sigma_{x}^{2}, \bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor

Craquelure as a Graph: Application of Image Processing and Graph Neural Networks to the Description of Fracture Patterns

Cracks on a painting is not a defect but an inimitable signature of an artwork which can be used for origin examination, aging monitoring, damage identification, and even forgery detection. This work presents the development of a new methodology and corresponding toolbox for the extraction and characterization of information from an image of a craquelure pattern. The proposed approach processes craquelure network as a graph. The graph representation captures the network structure via mutual organization of junctions and fractures. Furthermore, it is invariant to any geometrical distortions. At the same time, our tool extracts the properties of each node and edge individually, which allows to characterize the pattern statistically. We illustrate benefits from the graph representation and statistical features individually using novel Graph Neural Network and hand-crafted descriptors correspondingly. However, we also show that the best performance is achieved when both techniques are merged into one framework. We perform experiments on the dataset for paintings' origin classification and demonstrate that our approach outperforms existing techniques by a large margin.Comment: Published in ICCV 2019 Workshop

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Coding of details in very low bit-rate video systems

In this paper, the importance of including small image features at the initial levels of a progressive second generation video coding scheme is presented. It is shown that a number of meaningful small features called details should be coded, even at very low data bit-rates, in order to match their perceptual significance to the human visual system. We propose a method for extracting, perceptually selecting and coding of visual details in a video sequence using morphological techniques. Its application in the framework of a multiresolution segmentation-based coding algorithm yields better results than pure segmentation techniques at higher compression ratios, if the selection step fits some main subjective requirements. Details are extracted and coded separately from the region structure and included in the reconstructed images in a later stage. The bet of considering the local background of a given detail for its perceptual selection breaks the concept ofPeer ReviewedPostprint (published version

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1