New Guarantees for Blind Compressed Sensing

Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS) where the optimal sparsifying dictionary is assumed to be unknown and subject to estimation (in addition to the CS sparse coefficients). Since the emergence of BCS, dictionary learning, a.k.a. sparse coding, has been studied as a matrix factorization problem where its sample complexity, uniqueness and identifiability have been addressed thoroughly. However, in spite of the strong connections between BCS and sparse coding, recent results from the sparse coding problem area have not been exploited within the context of BCS. In particular, prior BCS efforts have focused on learning constrained and complete dictionaries that limit the scope and utility of these efforts. In this paper, we develop new theoretical bounds for perfect recovery for the general unconstrained BCS problem. These unconstrained BCS bounds cover the case of overcomplete dictionaries, and hence, they go well beyond the existing BCS theory. Our perfect recovery results integrate the combinatorial theories of sparse coding with some of the recent results from low-rank matrix recovery. In particular, we propose an efficient CS measurement scheme that results in practical recovery bounds for BCS. Moreover, we discuss the performance of BCS under polynomial-time sparse coding algorithms.Comment: To appear in the 53rd Annual Allerton Conference on Communication, Control and Computing, University of Illinois at Urbana-Champaign, IL, USA, 201

RPCA-KFE: Key Frame Extraction for Consumer Video based Robust Principal Component Analysis

Key frame extraction algorithms consider the problem of selecting a subset of the most informative frames from a video to summarize its content.Comment: This paper has been withdrawn by the author due to a crucial sign error in equation

Strong-Weak Integrated Semi-supervision for Unsupervised Single and Multi Target Domain Adaptation

Unsupervised domain adaptation (UDA) focuses on transferring knowledge learned in the labeled source domain to the unlabeled target domain. Despite significant progress that has been achieved in single-target domain adaptation for image classification in recent years, the extension from single-target to multi-target domain adaptation is still a largely unexplored problem area. In general, unsupervised domain adaptation faces a major challenge when attempting to learn reliable information from a single unlabeled target domain. Increasing the number of unlabeled target domains further exacerbate the problem rather significantly. In this paper, we propose a novel strong-weak integrated semi-supervision (SWISS) learning strategy for image classification using unsupervised domain adaptation that works well for both single-target and multi-target scenarios. Under the proposed SWISS-UDA framework, a strong representative set with high confidence but low diversity target domain samples and a weak representative set with low confidence but high diversity target domain samples are updated constantly during the training process. Both sets are fused to generate an augmented strong-weak training batch with pseudo-labels to train the network during every iteration. The extension from single-target to multi-target domain adaptation is accomplished by exploring the class-wise distance relationship between domains and replacing the strong representative set with much stronger samples from peer domains via peer scaffolding. Moreover, a novel adversarial logit loss is proposed to reduce the intra-class divergence between source and target domains, which is back-propagated adversarially with a gradient reverse layer between the classifier and the rest of the network. Experimental results based on three benchmarks, Office-31, Office-Home, and DomainNet, show the effectiveness of the proposed SWISS framework

Kovalenko's Full-Rank Limit and Overhead as Lower Bounds for Error-Performances of LDPC and LT Codes over Binary Erasure Channels

We present Kovalenko's full-rank limit as a tight lower bound for decoding error probability of LDPC codes and LT codes over BEC. From the limit, we derive a full-rank overhead as a lower bound for stable overheads for successful maximum-likelihood decoding of the codes.Comment: A short version of this paper was presented at ISITA 2008, Auckland NZ. The first draft was submitted to IEEE Transactions on Information Theory, 2008/0