Gaussian states under coarse-grained continuous variable measurements

The quantum-to-classical transition of a quantum state is a topic of great interest in fundamental and practical aspects. A coarse-graining in quantum measurement has recently been suggested as its possible account in addition to the usual decoherence model. We here investigate the reconstruction of a Gaussian state (single mode and two modes) by coarse-grained homodyne measurements. To this aim, we employ two methods, the direct reconstruction of the covariance matrix and the maximum likelihood estimation (MLE), respectively, and examine the reconstructed state under each scheme compared to the state interacting with a Gaussian (squeezed thermal) reservoir. We clearly demonstrate that the coarse-graining model, though applied equally to all quadrature amplitudes, is not compatible with the decoherence model by a thermal (phase-insensitive) reservoir. Furthermore, we compare the performance of the direct reconstruction and the MLE methods by investigating the fidelity and the nonclassicality of the reconstructed states and show that the MLE method can generally yield a more reliable reconstruction, particularly without information on a reference frame (phase of input state).Comment: published version, 9 pages, 5 figure

CARNet:Compression Artifact Reduction for Point Cloud Attribute

A learning-based adaptive loop filter is developed for the Geometry-based Point Cloud Compression (G-PCC) standard to reduce attribute compression artifacts. The proposed method first generates multiple Most-Probable Sample Offsets (MPSOs) as potential compression distortion approximations, and then linearly weights them for artifact mitigation. As such, we drive the filtered reconstruction as close to the uncompressed PCA as possible. To this end, we devise a Compression Artifact Reduction Network (CARNet) which consists of two consecutive processing phases: MPSOs derivation and MPSOs combination. The MPSOs derivation uses a two-stream network to model local neighborhood variations from direct spatial embedding and frequency-dependent embedding, where sparse convolutions are utilized to best aggregate information from sparsely and irregularly distributed points. The MPSOs combination is guided by the least square error metric to derive weighting coefficients on the fly to further capture content dynamics of input PCAs. The CARNet is implemented as an in-loop filtering tool of the GPCC, where those linear weighting coefficients are encapsulated into the bitstream with negligible bit rate overhead. Experimental results demonstrate significant improvement over the latest GPCC both subjectively and objectively.Comment: 13pages, 8figure

A Result About the Classification of Quantum Covariance Matrices Based on Their Eigenspectra

The set of covariance matrices of a continuous-variable quantum system with a finite number of degrees of freedom is a strict subset of the set of real positive-definite matrices due to Heisenberg's uncertainty principle. This has the implication that, in general, not every orthogonal transform of a quantum covariance matrix produces a positive-definite matrix that obeys the uncertainty principle. A natural question thus arises, to find the set of quantum covariance matrices consistent with a given eigenspectrum. For the special class of pure Gaussian states the set of quantum covariance matrices with a given eigenspectrum consists of a single orbit of the action of the orthogonal symplectic group. The eigenspectrum of a covariance matrix of a state in this class is composed of pairs that each multiply to one. Our main contribution is finding a non-trivial class of eigenspectra with the property that the set of quantum covariance matrices corresponding to any eigenspectrum in this class are related by orthogonal symplectic transformations. We show that all non-degenerate eigenspectra with this property must belong to this class, and that the set of such eigenspectra coincides with the class of non-degenerate eigenspectra that identify the physically relevant thermal and squeezing parameters of a Gaussian state

Model-based encoding parameter optimization for 3D point cloud compression

Rate-distortion optimal 3D point cloud compression is very challenging due to the irregular structure of 3D point clouds. For a popular 3D point cloud codec that uses octrees for geometry compression and JPEG for color compression, we first find analytical models that describe the relationship between the encoding parameters and the bitrate and distortion, respectively. We then use our models to formulate the rate-distortion optimization problem as a constrained convex optimization problem and apply an interior point method to solve it. Experimental results for six 3D point clouds show that our technique gives similar results to exhaustive search at only about 1.57% of its computational cost

Model-based joint bit allocation between geometry and color for video-based 3D point cloud compression

The file attached to this record is the author's final peer reviewed version.In video-based 3D point cloud compression, the quality of the reconstructed 3D point cloud depends on both the geometry and color distortions. Finding an optimal allocation of the total bitrate between the geometry coder and the color coder is a challenging task due to the large number of possible solutions. To solve this bit allocation problem, we first propose analytical distortion and rate models for the geometry and color information. Using these models, we formulate the joint bit allocation problem as a constrained convex optimization problem and solve it with an interior point method. Experimental results show that the rate distortion performance of the proposed solution is close to that obtained with exhaustive search but at only 0.66% of its time complexity

Codificação das cores de uma point cloud através da sua divisão em filamentos

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2018.Point cloud, ou nuvem de pontos, é uma representação tridimensional de uma cena que é possível ser visualizada por qualquer ângulo desejado. É uma tecnologia cuja captura está sendo cada vez mais desenvolvida e para que possa ser difundida em diversas apli- cações na sociedade é necessário o aprimoramento de seu processamento e codificação. Assim, nesse trabalho será desenvolvido um codificador sem perdas das cores de uma point cloud completo, que consiste em dividir a point cloud em camadas, segmentar as camadas em filamentos unidimensionais e codificar as cores desses filamentos através da codificação diferencial e de Huffman. O trabalho desenvolvido não depende da forma que a geometria da point cloud é codificada, permitindo que uma vez que o destinatário tenha a geometria seja possível decodificar gerando exatamente os mesmos filamentos realizados na codificação e a codificação gerada é sem perdas, podendo ser interessante para apli- cações que não tolerem perda de informação. Os resultados obtidos foram promissores, a taxa de compressão atingida média foi de 10 para 1, considerando o tamanho da point cloud como um todo e não só suas cores. Comparando com o codificador com perdas RAHT, que hoje é considerado o estado-da-arte na compressão de cores de uma point cloud, com um valor de parâmetro pequeno suficiente para que a imagem codificada seja o mais próximo da imagem original, o algortimo desenvolvido consegue gerar um arquivo menor e sem perdas, fazendo com que o trabalho possa ser competitivo com os devidos aprimoramentos. As possíveis melhorias futuras no trabalho desenvolvido se extendem desde a otimização na segmentação dos cortes para gerar os filamentos até a forma como as cores são codificadas e escritas no arquivo final.Point clouds are a three-dimensional representation of a scene that can be viewed by any desired angle. It is a technology whose capture is being improved considerably and for it to be diffused in diverse applications in society it is necessary to improve its processing and codification. In this work we will develop a complete lossless color encoder for point clouds, which consists of dividing the point cloud into layers and then segment these layers into one-dimensional filaments, encoding the colors from these filaments with Huffman and differential encoding. One of the merits of the work developed is that it does not depend on the way that the geometry of the point cloud is coded, allowing the use of other methods in the coding of the geometry of the point cloud. It also is a lossless method, allowing the use of this work for applications that cannot afford lossy methods for the used data. The results obtained were promissing, the average data compression ratio was 10 to 1, considering the size of the pointcloud as a whole, not only its colors. Comparing with the lossy encoder RAHT, which is considered the state of the art in color compression for point clouds, with a small enough parameter value for RAHT, making the coded image to be closest to he original imagem, our algorithm is able to generate a lossless smaller file, being able to be competitive with the appropriate improvements. One of the possible future improvements with the work that was developed is to find a better way for the segmentation of the layers or even changing the methodology used for coding the colors from the filaments, amongst other things

Transformées basées graphes pour la compression de nouvelles modalités d’image

Due to the large availability of new camera types capturing extra geometrical information, as well as the emergence of new image modalities such as light fields and omni-directional images, a huge amount of high dimensional data has to be stored and delivered. The ever growing streaming and storage requirements of these new image modalities require novel image coding tools that exploit the complex structure of those data. This thesis aims at exploring novel graph based approaches for adapting traditional image transform coding techniques to the emerging data types where the sampled information are lying on irregular structures. In a first contribution, novel local graph based transforms are designed for light field compact representations. By leveraging a careful design of local transform supports and a local basis functions optimization procedure, significant improvements in terms of energy compaction can be obtained. Nevertheless, the locality of the supports did not permit to exploit long term dependencies of the signal. This led to a second contribution where different sampling strategies are investigated. Coupled with novel prediction methods, they led to very prominent results for quasi-lossless compression of light fields. The third part of the thesis focuses on the definition of rate-distortion optimized sub-graphs for the coding of omni-directional content. If we move further and give more degree of freedom to the graphs we wish to use, we can learn or define a model (set of weights on the edges) that might not be entirely reliable for transform design. The last part of the thesis is dedicated to theoretically analyze the effect of the uncertainty on the efficiency of the graph transforms.En raison de la grande disponibilité de nouveaux types de caméras capturant des informations géométriques supplémentaires, ainsi que de l'émergence de nouvelles modalités d'image telles que les champs de lumière et les images omnidirectionnelles, il est nécessaire de stocker et de diffuser une quantité énorme de hautes dimensions. Les exigences croissantes en matière de streaming et de stockage de ces nouvelles modalités d’image nécessitent de nouveaux outils de codage d’images exploitant la structure complexe de ces données. Cette thèse a pour but d'explorer de nouvelles approches basées sur les graphes pour adapter les techniques de codage de transformées d'image aux types de données émergents où les informations échantillonnées reposent sur des structures irrégulières. Dans une première contribution, de nouvelles transformées basées sur des graphes locaux sont conçues pour des représentations compactes des champs de lumière. En tirant parti d’une conception minutieuse des supports de transformées locaux et d’une procédure d’optimisation locale des fonctions de base , il est possible d’améliorer considérablement le compaction d'énergie. Néanmoins, la localisation des supports ne permettait pas d'exploiter les dépendances à long terme du signal. Cela a conduit à une deuxième contribution où différentes stratégies d'échantillonnage sont étudiées. Couplés à de nouvelles méthodes de prédiction, ils ont conduit à des résultats très importants en ce qui concerne la compression quasi sans perte de champs de lumière statiques. La troisième partie de la thèse porte sur la définition de sous-graphes optimisés en distorsion de débit pour le codage de contenu omnidirectionnel. Si nous allons plus loin et donnons plus de liberté aux graphes que nous souhaitons utiliser, nous pouvons apprendre ou définir un modèle (ensemble de poids sur les arêtes) qui pourrait ne pas être entièrement fiable pour la conception de transformées. La dernière partie de la thèse est consacrée à l'analyse théorique de l'effet de l'incertitude sur l'efficacité des transformées basées graphes

Saliency-driven dynamic point cloud coding using projections onto images

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2021.As regiões de interesse (ROI) têm sido utilizadas na codicação tradicional de imagens e vídeos para melhorar a qualidade do quadro em certas regiões, como rostos, em detrimento de outras áreas. No entanto, a ROI na compressão de nuvens de pontos não foi amplamente abordada, as- sim como a criação de mapas de saliência. Ambos os pontos são abordados neste trabalho. É difícil identicar diretamente atributos como rostos em nuvens de pontos esparsas e foi desenvolvido um método alternativo para o fazer. São utilizadas projeções ortográcas em planos 2D que são sub- metidas a algoritmos de visão computacional bem conhecidos. Uma vez identicada uma região de interesse, os seus pixels são retroprojetados nos voxels correspondentes. Ao repetir as projeções ao longo de muitas vistas, a informação de múltiplas projeções é agregada para formar um conjunto de voxels que se acredita conter a ROI ou serem os com maior valor de saliência. Como método não supervisionado, foi concebido um algoritmo para procurar as melhores vistas para projeções, utilizando informação de consistência temporal que é herdada de um quadro para outro. Foram utilizados algoritmos de detecção facial, tais como Viola-Jones, para determinar a ROI 2D e foram também utilizados algoritmos de criação de mapas de saliências bem estabelecidos para imagens bidimensionais. A m de utilizar a ROI para compressão, foi desenvolvida uma estratégia de codi- cação baseada num critério de distorção modicada que pode ser aplicado a muitos codicadores e é naturalmente aplicável ao codicador que utiliza a transformação hierárquica por região adap- tável (RAHT). Na sua essência, os bits (e a qualidade) são deslocados para a ROI a partir de áreas não-ROI, assumindo que as partes não-ROI são visualmente menos importantes e têm valores de saliência inferiores. Os resultados revelam uma grande melhoria subjetiva global ao melhorar con- sideravelmente o ROI à custa de uma pequena degradação das regiões de menor saliência.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).Regions of interest (ROI) have been used in traditional image and video coding to improve im- age quality in certain regions, like faces, at the expense of other areas. Nevertheless, ROI in point cloud compression have not been properly addressed, nor has the creation of saliency maps. Both points are addressed in this work. It is hard to directly identify features such as faces in unconnected point clouds and an alternative method to do so was developed. Orthographic projections in 2D planes which are subject to well established computer vision algorithms are used. Once an image region is identied, their pixels are back-projected onto the corresponding voxels. By repeating the projections over many orientations, the information of the many back projections is fused to form a collection of voxels believed to contain the ROI or to be the most salient. As an unsupervised method, it was devised an algorithm to search the projection orientations for the best views, which include temporal consistency information which is inherited from one frame to another. Face de- tection algorithms, such as Viola-Jones, were used to determine the 2D ROI and well established saliency map creation algorithms were also used in the 2D image case. In order to use ROI for com- pression, it was developed an encoding strategy based on a modied distortion criterion that can be applied to many coders and is naturally applicable to the region-adaptive hierarchical transform (RAHT) based coder, which is being adapted into compression standards. In essence, bits (and quality) are shifted towards the ROI from non-ROI areas, assuming non-ROI parts are visually less important and have lower salience values. Results reveal large overall subjective improvement by greatly improving the ROI at the expense of a small degradation of textured regions of lower salience