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In this work we propose a method for estimating disparity maps from very few measurements. Based on the theory of Compressive Sensing, our algorithm accurately reconstructs disparity maps only using about 5% of the entire map. We propose a conjugate subgradient method for the arising optimization problem that is applicable to large scale systems and… (More)

Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), K-means clustering, etc., rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. While the idealized task would be to… (More)

Exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems. The synthesis model, which assumes that images can be decomposed into a linear combination of very few atoms of some dictionary, is now a well established tool for the design of image reconstruction algorithms. An… (More)

Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a suitable training set. While analytic dictionaries permit to capture the global structure of a signal and allow a fast… (More)

High-resolution depth maps can be inferred from low-resolution depth measurements and an additional high-resolution intensity image of the same scene. To that end, we introduce a bimodal co-sparse analysis model, which is able to capture the interdependency of registered intensity and depth information. This model is based on the assumption that the… (More)

An increasing number of methods for background subtraction use Robust PCA to identify sparse foreground objects. While many algorithms use the 1-norm as a convex relaxation of the ideal sparsifying function, we approach the problem with a smoothed p-norm and present pROST, a method for robust online subspace tracking. The algorithm is based on alternating… (More)

In this paper, we address the problem of complex blind source separation (BSS), in particular, separation of nonstationary complex signals. It is known that, under certain conditions, complex BSS can be solved effectively by the so-called Strong Uncorrelating Transform (SUT), which simultaneously diagonalizes one Hermitian positive definite and one complex… (More)

The FastICA algorithm is one of the most prominent methods to solve the problem of linear independent component analysis (ICA). Although there have been several attempts to prove local convergence properties of FastICA, rigorous analysis is still missing in the community. The major difficulty of analysis is because of the well-known sign-flipping phenomenon… (More)

This work studies the problem of simultaneously separating and reconstructing signals from compressively sensed linear mixtures. We assume that all source signals share a common sparse representation basis. The approach combines classical Compressive Sensing (CS) theory with a linear mixing model. It allows the mixtures to be sampled independently of each… (More)

In this paper, a conjugate gradient method on the complex Graßmann manifold is proposed that computes the k-principal components of a Hermitian (n×n)-matrix. The algorithm is at most of order O(n 2 k) and yields locally good convergence results.