A New Approach to Sparse Image Representation Using MMV and K-SVD

This paper addresses the problem of image representation based on a sparse decomposition over a learned dictionary. We propose an improved matching pursuit algorithm for Multiple Measurement Vectors (MMV) and an adaptive algorithm for dictionary learning based on multi-Singular Value Decomposition (SVD), and combine them for image representation. Compared with the traditional K-SVD and orthogonal matching pursuit MMV (OMPMMV) methods, the proposed method runs faster and achieves a higher overall reconstruction accuracy

Unitary Approximate Message Passing for Sparse Bayesian Learning and Bilinear Recovery

Over the past several years, the approximate message passing (AMP) algorithm has been applied to a broad range of problems, including compressed sensing (CS), robust regression, Bayesian estimation, etc. AMP was originally developed for compressed sensing based on the loopy belief propagation (BP). Compared to convex optimization based algorithms, AMP has low complexity and its performance can be rigorously characterized by a scalar state evolution (SE) in the case of a large independent and identically distributed (i.i.d.) (sub-) Gaussian matrix. AMP was then extended to solve general estimation problems with a generalized linear observation model. However, AMP performs poorly on a generic matrix such as non-zero mean, rank-deficient, correlated, or ill-conditioned matrix, resulting in divergence and degraded performance. It was discovered later that applying AMP to a unitary transform of the original model can remarkably enhance the robustness to difficult matrices. This variant is named unitary AMP (UAMP), or formally called UTAMP. In this thesis, leveraging UAMP, we propose UAMP-SBL for sparse signal recovery and Bi-UAMP for bilinear recovery, both of which inherit the low complexity and robustness of UAMP. Sparse Bayesian learning (SBL) is a powerful tool for recovering a sparse signal from noisy measurements, which finds numerous applications in various areas. As a traditional implementation of SBL, e.g., Tipping’s method, involves matrix inversion in each iteration, the computational complexity can be prohibitive for large scale problems. To circumvent this, AMP and its variants have been used as low-complexity solutions. Unfortunately, they will diverge for ‘difficult’ measurement matrices as previously mentioned. In this thesis, leveraging UAMP, a novel SBL algorithm called UAMP-SBL is proposed where UAMP is incorporated into the structured variational message passing (SVMP) to handle the most computationally intensive part of message computations. It is shown that, compared to state-of-the-art AMP based SBL algorithms, the proposed UAMP-SBL is more robust and efficient, leading to remarkably better performance. The bilinear recovery problem has many applications such as dictionary learning, selfcalibration, compressed sensing with matrix uncertainty, etc. Compared to existing nonmessage passing alternates, several AMP based algorithms have been developed to solve bilinear problems. By using UAMP, a more robust and faster approximate inference algorithm for bilinear recovery is proposed in this thesis, which is called Bi-UAMP. With the lifting approach, the original bilinear problem is reformulated as a linear one. Then, variational inference (VI), expectation propagation (EP) and BP are combined with UAMP to implement the approximate inference algorithm Bi-UAMP, where UAMP is adopted for the most computationally intensive part. It is shown that, compared to state-of-the-art bilinear recovery algorithms, the proposed Bi-UAMP is much more robust and faster, and delivers significantly better performance. Recently, UAMP has also been employed for many other applications such as inverse synthetic aperture radar (ISAR) imaging, low-complexity direction of arrival (DOA) estimation, iterative detection for orthogonal time frequency space modulation (OTFS), channel estimation for RIS-Aided MIMO communications, etc. Promising performance was achieved in all of the applications, and more applications of UAMP are expected in the future

K-Space at TRECVid 2007

In this paper we describe K-Space participation in TRECVid 2007. K-Space participated in two tasks, high-level feature extraction and interactive search. We present our approaches for each of these activities and provide a brief analysis of our results. Our high-level feature submission utilized multi-modal low-level features which included visual, audio and temporal elements. Specific concept detectors (such as Face detectors) developed by K-Space partners were also used. We experimented with different machine learning approaches including logistic regression and support vector machines (SVM). Finally we also experimented with both early and late fusion for feature combination. This year we also participated in interactive search, submitting 6 runs. We developed two interfaces which both utilized the same retrieval functionality. Our objective was to measure the effect of context, which was supported to different degrees in each interface, on user performance. The first of the two systems was a ‘shot’ based interface, where the results from a query were presented as a ranked list of shots. The second interface was ‘broadcast’ based, where results were presented as a ranked list of broadcasts. Both systems made use of the outputs of our high-level feature submission as well as low-level visual features