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We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have superseded them in terms of rate–distortion performance under established perceptual quality metrics such as MS-SSIM. We assess the empirical rate–distortion performance of NTC with the help of simple example sources, for which the optimal performance of a vector quantizer is easier to estimate than with natural data sources. To this end, we introduce a novel variant of entropy-constrained vector quantization. We provide an analysis of various forms of stochastic optimization techniques for NTC models; review architectures of transforms based on artificial neural networks, as well as learned entropy models; and provide a direct comparison of a number of methods to parameterize the rate–distortion trade-off of nonlinear transforms, introducing a simplified one. [ABSTRACT FROM AUTHOR]

Objectives To evaluate facial attractiveness of treated cleft patients and controls by artificial intelligence (AI) and to compare these results with panel ratings performed by laypeople, orthodontists, and oral surgeons. Materials and methods Frontal and profile images of 20 treated left-sided cleft patients (10 males, mean age: 20.5 years) and 10 controls (5 males, mean age: 22.1 years) were evaluated for facial attractiveness with dedicated convolutional neural networks trained on >17 million ratings for attractiveness and compared to the assessments of 15 laypeople, 14 orthodontists, and 10 oral surgeons performed on a visual analogue scale (n = 2323 scorings). Results AI evaluation of cleft patients (mean score: 4.75 ± 1.27) was comparable to human ratings (laypeople: 4.24 ± 0.81, orthodontists: 4.82 ± 0.94, oral surgeons: 4.74 ± 0.83) and was not statistically different (all P s ≥ 0.19). Facial attractiveness of controls was rated significantly higher by humans than AI (all P s ≤ 0.02), which yielded lower scores than in cleft subjects. Variance was considerably large in all human rating groups when considering cases separately, and especially accentuated in the assessment of cleft patients (coefficient of variance—laypeople: 38.73 ± 9.64, orthodontists: 32.56 ± 8.21, oral surgeons: 42.19 ± 9.80). Conclusions AI-based results were comparable with the average scores of cleft patients seen in all three rating groups (with especially strong agreement to both professional panels) but overall lower for control cases. The variance observed in panel ratings revealed a large imprecision based on a problematic absence of unity. Implication Current panel-based evaluations of facial attractiveness suffer from dispersion-related issues and remain practically unavailable for patients. AI could become a helpful tool to describe facial attractiveness, but the present results indicate that important adjustments are needed on AI models, to improve the interpretation of the impact of cleft features on facial attractiveness. [ABSTRACT FROM AUTHOR]

We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals, modeled as general random vectors, from the noiseless sum of linear measurements of the signals. Our framework is inspired by the groundbreaking work of Wu and Verdú (2010) on analog compression and encompasses, inter alia, inpainting, declipping, super-resolution, the recovery of signals corrupted by impulse noise, and the separation of (e.g., audio or video) signals into two distinct components. The main results we report are general achievability bounds for the compression rate, i.e., the number of measurements relative to the dimension of the ambient space the signals live in, under either measurability or Hölder continuity imposed on the separator. Furthermore, we find a matching converse for sources of mixed discrete-continuous distribution. For measurable separators our proofs are based on a new probabilistic uncertainty relation, which shows that the intersection of generic subspaces with general sets of sufficiently small Minkowski dimension is empty. Hölder continuous separators are dealt with by introducing the concept of regularized probabilistic uncertainty relations. The probabilistic uncertainty relations we develop are inspired by embedding results in dynamical systems theory due to Sauer et al. (1991) and—conceptually—parallel classical Donoho-Stark and Elad-Bruckstein uncertainty principles at the heart of compressed sensing theory. Operationally, the new uncertainty relations take the theory of sparse signal separation beyond traditional sparsity—as measured in terms of the number of non-zero entries—to the more general notion of low description complexity as quantified by Minkowski dimension. Finally, our approach also allows to significantly strengthen key results in Wu and Verdú (2010). [ABSTRACT FROM AUTHOR]