Subspace Representations and Learning for Visual Recognition

Pervasive and affordable sensor and storage technology enables the acquisition of an ever-rising amount of visual data. The ability to extract semantic information by interpreting, indexing and searching visual data is impacting domains such as surveillance, robotics, intelligence, human- computer interaction, navigation, healthcare, and several others. This further stimulates the investigation of automated extraction techniques that are more efficient, and robust against the many sources of noise affecting the already complex visual data, which is carrying the semantic information of interest. We address the problem by designing novel visual data representations, based on learning data subspace decompositions that are invariant against noise, while being informative for the task at hand. We use this guiding principle to tackle several visual recognition problems, including detection and recognition of human interactions from surveillance video, face recognition in unconstrained environments, and domain generalization for object recognition.;By interpreting visual data with a simple additive noise model, we consider the subspaces spanned by the model portion (model subspace) and the noise portion (variation subspace). We observe that decomposing the variation subspace against the model subspace gives rise to the so-called parity subspace. Decomposing the model subspace against the variation subspace instead gives rise to what we name invariant subspace. We extend the use of kernel techniques for the parity subspace. This enables modeling the highly non-linear temporal trajectories describing human behavior, and performing detection and recognition of human interactions. In addition, we introduce supervised low-rank matrix decomposition techniques for learning the invariant subspace for two other tasks. We learn invariant representations for face recognition from grossly corrupted images, and we learn object recognition classifiers that are invariant to the so-called domain bias.;Extensive experiments using the benchmark datasets publicly available for each of the three tasks, show that learning representations based on subspace decompositions invariant to the sources of noise lead to results comparable or better than the state-of-the-art

Learning Partially Shared Dictionaries for Domain Adaptation

Abstract. Real world applicability of many computer vision solutions is constrained by the mismatch between the training and test domains. This mismatch might arise because of factors such as change in pose, lighting conditions, quality of imaging devices, intra-class variations in-herent in object categories etc. In this work, we present a dictionary learning based approach to tackle the problem of domain mismatch. In our approach, we jointly learn dictionaries for the source and the target domains. The dictionaries are partially shared, i.e. some elements are common across both the dictionaries. These shared elements can rep-resent the information which is common across both the domains. The dictionaries also have some elements to represent the domain specific information. Using these dictionaries, we separate the domain specific information and the information which is common across the domains. We use the latter for training cross-domain classifiers i.e., we build classi-fiers that work well on a new target domain while using labeled examples only in the source domain. We conduct cross-domain object recognition experiments on popular benchmark datasets and show improvement in results over the existing state of art domain adaptation approaches.

The Geometry of Uniqueness, Sparsity and Clustering in Penalized Estimation

We provide a necessary and sufficient condition for the uniqueness of penalized least-squares estimators whose penalty term is given by a norm with a polytope unit ball, covering a wide range of methods including SLOPE and LASSO, as well as the related method of basis pursuit. We consider a strong type of uniqueness that is relevant for statistical problems. The uniqueness condition is geometric and involves how the row span of the design matrix intersects the faces of the dual norm unit ball, which for SLOPE is given by the sign permutahedron. Further considerations based this condition also allow to derive results on sparsity and clustering features. In particular, we define the notion of a SLOPE model to describe both sparsity and clustering properties of this method and also provide a geometric characterization of accessible SLOPE models.Comment: new title, minor change

Detection of sparse targets with structurally perturbed echo

Cataloged from PDF version of article.In this paper, a novel algorithm is proposed to achieve robust high resolution detection in sparse multipath channels. Currently used sparse reconstruction techniques are not immediately applicable in multipath channel modeling. Performance of standard compressed sensing formulations based on discretization of the multipath channel parameter space degrade significantly when the actual channel parameters deviate from the assumed discrete set of values. To alleviate this off-grid problem, we make use of the particle swarm optimization (PSO) to perturb each grid point that reside in each multipath component cluster. Orthogonal matching pursuit (OMP) is used to reconstruct sparse multipath components in a greedy fashion. Extensive simulation results quantify the performance gain and robustness obtained by the proposed algorithm against the off-grid problem faced in sparse multipath channels. © 2013 Elsevier Inc

Millimeter wave link configuration with hybrid MIMO architectures

The use of multiple antennas, widely known as MIMO technology, is a key feature to deploy mmWave communication systems enabling high-data-rate applications. With more than two decades of global experience in deploying Wi-Fi and cellular communication using sub-6 GHz frequency bands, simply repurposing these designs for mmWave bands would fail to account for additional propagation impairments and circuit design constraints at these higher frequencies. A solution to overcome the propagation challenges is the use of multiple directional communication beams, whereby proper alignment between transceivers provides sufficient link quality to enable reliable decoding of the transmitted data. In this dissertation, efficient link configuration solutions suitable for mmWave cellular communications are developed. To gain some insight into the achievable performance of mmWave systems, two broadband channel-estimation-based link configuration solutions are proposed for MIMO-OFDM systems, in which both the transmitter and receiver are assumed to be perfectly synchronized. The proposed solution exploits the spatially common sparsity in the mmWave channel and enables efficient acquisition of the CSI while allowing the use of multiple RF chains on both the transmitter and receiver sides. In a simplified scenario, the CRLB for the channel estimation problem is derived, and the proposed channel estimation algorithms are shown to both outperform prior work in communication performance and exhibit excellent estimation performance. Furthermore, the proposed algorithms are assessed in a more challenging scenario with realistic channel parameters, and it is shown that both near-optimal spectral efficiency and low BER can be attained with lower overhead and computational complexity than prior solutions. Next, the impact of imperfect CFO synchronization on the channel estimation problem is analyzed under a narrowband channel model. The CRLB for the estimation of the different unknown parameters involved in the problem is theoretically analyzed, and closed-form expressions are provided for the estimation of the different parameters. Under a joint estimation-theoretic and CS framework, a low-complexity multi-stage solution is proposed to estimate both the different unknown synchronization parameters and the large-dimensional mmWave MIMO channel. Different trade-offs between estimation, spectral efficiency, and overhead performance are exposed, and the proposed estimators are shown to be asymptotically optimal in the low SNR regime. The proposed solution is assessed under a channel model with several clusters and rays per cluster, and is shown to attain near-optimal spectral efficiency values in both the low and high SNR regimes. The computational complexity of the proposed solution is also analyzed, in which it is shown to achieve a marginal increase in computational complexity with respect to the solution proposed in the previous contribution. Finally, the impact of TO, CFO, and PN impairments on the channel estimation problem is analyzed under a broadband channel model. The problem of time-frequency synchronization under PN impairments is theoretically analyzed, and the proposed solutions to the synchronization problem are exploited to estimate the frequency-selective mmWave MIMO channel. The hybrid CRLB for the estimation of the different synchronization impairments is analyzed, and closed-form expressions leveraging the information coupling between the different impairments are provided. The previously proposed joint estimation-theoretic and CS framework is extended to frequency-selective scenarios, and two low-complexity multi-stage solutions are proposed to estimate both the different synchronization impairments and the large-dimensional mmWave MIMO channel. The first solution relies on a batch-processing LMMSE-based EM algorithm to estimate the different synchronization impairments, while the second solution uses a sequential-processing EKF-RTS-based EM algorithm, thereby reducing computational complexity. Thereafter, both the hybrid CRLB for the estimation of the equivalent beamformed complex channels and the estimates for these parameters are exploited to estimate the large-dimensional frequency-selective mmWave MIMO channel. Finally, a joint PN and data detection algorithm is proposed for data transmission under the 5G NR frame structure. The proposed solutions are evaluated using a 5G NR-based channel model, and different trade-offs between estimation performance, computational complexity, overhead, achievable spectral efficiency and BER are exposed, and comparisons with prior work are also provided. The results show that mmWave link configuration using hybrid MIMO architectures can be established with low overhead without assuming synchronization, even in the low SNR regime.Electrical and Computer Engineerin