Invertible Rescaling Network and Its Extensions

Image rescaling is a commonly used bidirectional operation, which first downscales high-resolution images to fit various display screens or to be storage- and bandwidth-friendly, and afterward upscales the corresponding low-resolution images to recover the original resolution or the details in the zoom-in images. However, the non-injective downscaling mapping discards high-frequency contents, leading to the ill-posed problem for the inverse restoration task. This can be abstracted as a general image degradation-restoration problem with information loss. In this work, we propose a novel invertible framework to handle this general problem, which models the bidirectional degradation and restoration from a new perspective, i.e. invertible bijective transformation. The invertibility enables the framework to model the information loss of pre-degradation in the form of distribution, which could mitigate the ill-posed problem during post-restoration. To be specific, we develop invertible models to generate valid degraded images and meanwhile transform the distribution of lost contents to the fixed distribution of a latent variable during the forward degradation. Then restoration is made tractable by applying the inverse transformation on the generated degraded image together with a randomly-drawn latent variable. We start from image rescaling and instantiate the model as Invertible Rescaling Network (IRN), which can be easily extended to the similar decolorization-colorization task. We further propose to combine the invertible framework with existing degradation methods such as image compression for wider applications. Experimental results demonstrate the significant improvement of our model over existing methods in terms of both quantitative and qualitative evaluations of upscaling and colorizing reconstruction from downscaled and decolorized images, and rate-distortion of image compression.Comment: Accepted by IJC

Faithful extreme rescaling via generative prior reciprocated invertible representations

This paper presents a Generative prior ReciprocAted Invertible rescaling Network (GRAIN) for generating faithful high-resolution (HR) images from low-resolution (LR) invertible images with an extreme upscaling factor (64$\times$). Previous researches have leveraged the prior knowledge of a pretrained GAN model to generate high-quality upscaling results. However, they fail to produce pixel-accurate results due to the highly ambiguous extreme mapping process. We remedy this problem by introducing a reciprocated invertible image rescaling process, in which high-resolution information can be delicately embedded into an invertible low-resolution image and generative prior for a faithful HR reconstruction. In particular, the invertible LR features not only carry significant HR semantics, but also are trained to predict scale-specific latent codes, yielding a preferable utilization of generative features. On the other hand, the enhanced generative prior is re-injected to the rescaling process, compensating the lost details of the invertible rescaling. Our reciprocal mechanism perfectly integrates the advantages of invertible encoding and generative prior, leading to the first feasible extreme rescaling solution. Extensive experiments demonstrate superior performance against state-of-the-art upscaling methods. Code is available at https://github.com/cszzx/GRAIN

Self-Asymmetric Invertible Network for Compression-Aware Image Rescaling

High-resolution (HR) images are usually downscaled to low-resolution (LR) ones for better display and afterward upscaled back to the original size to recover details. Recent work in image rescaling formulates downscaling and upscaling as a unified task and learns a bijective mapping between HR and LR via invertible networks. However, in real-world applications (e.g., social media), most images are compressed for transmission. Lossy compression will lead to irreversible information loss on LR images, hence damaging the inverse upscaling procedure and degrading the reconstruction accuracy. In this paper, we propose the Self-Asymmetric Invertible Network (SAIN) for compression-aware image rescaling. To tackle the distribution shift, we first develop an end-to-end asymmetric framework with two separate bijective mappings for high-quality and compressed LR images, respectively. Then, based on empirical analysis of this framework, we model the distribution of the lost information (including downscaling and compression) using isotropic Gaussian mixtures and propose the Enhanced Invertible Block to derive high-quality/compressed LR images in one forward pass. Besides, we design a set of losses to regularize the learned LR images and enhance the invertibility. Extensive experiments demonstrate the consistent improvements of SAIN across various image rescaling datasets in terms of both quantitative and qualitative evaluation under standard image compression formats (i.e., JPEG and WebP).Comment: Accepted by AAAI 2023. Code is available at https://github.com/yang-jin-hai/SAI

Invertible Mosaic Image Hiding Network for Very Large Capacity Image Steganography

The existing image steganography methods either sequentially conceal secret images or conceal a concatenation of multiple images. In such ways, the interference of information among multiple images will become increasingly severe when the number of secret images becomes larger, thus restrict the development of very large capacity image steganography. In this paper, we propose an Invertible Mosaic Image Hiding Network (InvMIHNet) which realizes very large capacity image steganography with high quality by concealing a single mosaic secret image. InvMIHNet consists of an Invertible Image Rescaling (IIR) module and an Invertible Image Hiding (IIH) module. The IIR module works for downscaling the single mosaic secret image form by spatially splicing the multiple secret images, and the IIH module then conceal this mosaic image under the cover image. The proposed InvMIHNet successfully conceal and reveal up to 16 secret images with a small number of parameters and memory consumption. Extensive experiments on ImageNet-1K, COCO and DIV2K show InvMIHNet outperforms state-of-the-art methods in terms of both the imperceptibility of stego image and recover accuracy of secret image

The moduli space of matroids

In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective matroid theories. Moreover, fuzzy rings are ordered blueprints and lie in the intersection of tracts with ordered blueprints; we call the objects of this intersection pastures. In the second part, we construct moduli spaces for matroids over pastures. We show that, for any non-empty finite set $E$, the functor taking a pasture $F$ to the set of isomorphism classes of rank-$r$ $F$-matroids on $E$ is representable by an ordered blue scheme $Mat(r,E)$, the moduli space of rank-$r$ matroids on $E$. In the third part, we draw conclusions on matroid theory. A classical rank-$r$ matroid $M$ on $E$ corresponds to a $\mathbb{K}$-valued point of $Mat(r,E)$ where $\mathbb{K}$ is the Krasner hyperfield. Such a point defines a residue pasture $k_M$, which we call the universal pasture of $M$. We show that for every pasture $F$, morphisms $k_M\to F$ are canonically in bijection with $F$-matroid structures on $M$. An analogous weak universal pasture $k_M^w$ classifies weak $F$-matroid structures on $M$. The unit group of $k_M^w$ can be canonically identified with the Tutte group of $M$. We call the sub-pasture $k_M^f$ of $k_M^w$ generated by ``cross-ratios' the foundation of $M$,. It parametrizes rescaling classes of weak $F$-matroid structures on $M$, and its unit group is coincides with the inner Tutte group of $M$. We show that a matroid $M$ is regular if and only if its foundation is the regular partial field, and a non-regular matroid $M$ is binary if and only if its foundation is the field with two elements. This yields a new proof of the fact that a matroid is regular if and only if it is both binary and orientable.Comment: 83 page

Blind Normalization of Speech From Different Channels

We show how to construct a channel-independent representation of speech that has propagated through a noisy reverberant channel. This is done by blindly rescaling the cepstral time series by a non-linear function, with the form of this scale function being determined by previously encountered cepstra from that channel. The rescaled form of the time series is an invariant property of it in the following sense: it is unaffected if the time series is transformed by any time-independent invertible distortion. Because a linear channel with stationary noise and impulse response transforms cepstra in this way, the new technique can be used to remove the channel dependence of a cepstral time series. In experiments, the method achieved greater channel-independence than cepstral mean normalization, and it was comparable to the combination of cepstral mean normalization and spectral subtraction, despite the fact that no measurements of channel noise or reverberations were required (unlike spectral subtraction).Comment: 25 pages, 7 figure

Quantum Lie algebras; their existence, uniqueness and qq-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules of the quantized enveloping algebras. On them the quantum Lie bracket is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g_h independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras are isomorphic to an abstract quantum Lie algebra g_h. In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras associated to the same g are isomorphic, 2) the quantum Lie bracket of any quantum Lie algebra is $q$-antisymmetric. We also describe a construction of quantum Lie algebras which establishes their existence.Comment: 18 pages, amslatex. Files also available from http://www.mth.kcl.ac.uk/~delius/q-lie/qlie_biblio/qlieuniq.htm