Mohammad Golbabaee

Hyperspectral image compressed sensing via low-rank and joint-sparse matrix recovery

We propose a novel approach to reconstruct Hyperspectral images from very few number of noisy compressive measurements. Our reconstruction approach is based on a convex minimization which penalizes both the nuclear norm and the ℓ2,1 mixed-norm of the data matrix. Thus, the solution tends to have a simultaneous low-rank and joint-sparse structure. We explain how these two assumptions fit Hyperspectral data, and by severals simulations we show that our proposed reconstruction scheme significantly enhances the state-of-the-art tradeoffs between the reconstruction error and the required number of CS measurements.

Compressive Source Separation: Theory and Methods for Hyperspectral Imaging

We propose and analyze a new model for hyperspectral images (HSIs) based on the assumption that the whole signal is composed of a linear combination of few sources, each of which has a specific spectral signature, and that the spatial abundance maps of these sources are themselves piecewise smooth and therefore efficiently encoded via typical sparse models. We derive new sampling schemes exploiting this assumption and give theoretical lower bounds on the number of measurements required to reconstruct HSI data and recover their source model parameters. This allows us to segment HSIs into their source abundance maps directly from compressed measurements. We also propose efficient optimization algorithms and perform extensive experimentation on synthetic and real datasets, which reveals that our approach can be used to encode HSI with far less measurements and computational effort than traditional compressive sensing methods.

Joint trace/TV norm minimization: A new efficient approach for spectral compressive imaging

In this paper we propose a novel and efficient model for compressed sensing of hyperspectral images. A large-size hyperspectral image can be subsampled by retaining only 3% of its original size, yet robustly recovered using the new approach we present here. Our reconstruction approach is based on minimizing a convex functional which penalizes both the trace norm and the TV norm of the data matrix. Thus, the solution tends to have a simultaneous low-rank and piecewise smooth structure: the two important priors explaining the underlying correlation structure of such data. Through simulations we will show our approach significantly enhances the conventional compression rate-distortion tradeoffs. In particular, in the strong undersampling regimes our method outperforms the standard TV denoising image recovery scheme by more than 17dB in the reconstruction MSE.

Light field compressive sensing in camera arrays

This paper presents a novel approach to capture light field in camera arrays based on the compressive sensing framework. Light fields are captured by a linear array of cameras with overlapping field of view. In this work, we design a redundant dictionary to exploit cross-cameras correlated structures to sparsely represent cameras image. Our main contributions are threefold. First, we exploit the correlations between the set of views by making use of a specially designed redundant dictionary. We show experimentally that the projection of complex scenes onto this dictionary yields very sparse coefficients. Second, we propose an efficient compressive encoding scheme based on the random convolution framework [1]. Finally, we develop a joint sparse recovery algorithm for decoding the compressed measurements and show a marked improvement over independent decoding of CS measurements.

SCOOP: A Real-Time Sparsity Driven People Localization Algorithm

Detecting and tracking people in scenes monitored by cameras is an important step in many application scenarios such as surveillance, urban planning or behavioral studies to name a few. The amount of data produced by camera feeds is so large that it is also vital that these steps be performed with the utmost computational efficiency and often even real-time. We propose SCOOP, a novel algorithm that reliably localizes people in camera feeds, using only the output of a simple background removal technique. SCOOP can handle a single or many video feeds. At the heart of our technique there is a sparse model for binary motion detection maps that we solve with a novel greedy algorithm based on set covering. We study the convergence and performance of the algorithm under various degradation models such as noisy observations and crowded environments, and we provide mathematical and experimental evidence of both its efficiency and robustness using standard datasets. This clearly shows that SCOOP is a viable alternative to existing state-of-the-art people localization algorithms, with the marked advantage of real-time computations.

Distributed compressed sensing of Hyperspectral images via blind source separation

This paper describes a novel framework for compressive sampling (CS) of multichannel signals that are highly dependent across the channels. In this work, we assume few number of sources are generating the multichannel observations based on a linear mixture model. Moreover, sources are assumed to have sparse/compressible representations in some orthonormal basis. The main contribution of this paper lies in 1) rephrasing the CS acquisition of multichannel data as a compressive blind source separation problem, and 2) proposing an optimization problem and a recovery algorithm to estimate both the sources and the mixing matrix (and thus the whole data) from the compressed measurements. A number of experiments on the acquisition of Hyperspectral images show that our proposed algorithm obtains a reconstruction error between 10 dB and 15 dB less than other state-of-the-art CS methods.

Numerical experiments with MALDI Imaging data

This article does not present new mathematical results, it solely aims at discussing some numerical experiments with MALDI Imaging data. However, these experiments are based on and could not be done without the mathematical results obtained in the UNLocX project. They tackle two obstacles which presently prevent clinical routine applications of MALDI Imaging technology. In the last decade, matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI-IMS) has developed into a powerful bioanalytical imaging modality. MALDI imaging data consists of a set of mass spectra, which are measured at different locations of a flat tissue sample. Hence, this technology is capable of revealing the full metabolic structure of the sample under investigation. Sampling resolution as well as spectral resolution is constantly increasing, presently a conventional 2D MALDI Imaging data requires up to 100 GB per dataset. A major challenge towards routine applications of MALDI Imaging in pharmaceutical or medical workflows is the high computational cost for evaluating and visualizing the information content of MALDI imaging data. This becomes even more critical in the near future when considering cohorts or 3D applications. Due to its size and complexity MALDI Imaging constitutes a challenging test case for high performance signal processing. In this article we will apply concepts and algorithms, which were developed within the UNLocX project, to MALDI Imaging data. In particular we will discuss a suitable phase space model for such data and report on implementations of the resulting transform coders using GPU technology. Within the MALDI Imaging workflow this leads to an efficient baseline removal and peak picking. The final goal of data processing in MALDI Imaging is the discrimination of regions having different metabolic structures. We introduce and discuss so-called soft-segmentation maps which are obtained by non-negative matrix factorization incorporating sparsity constraints.

Distributed Compressed Sensing for Sensor Networks Using Thresholding

Distributed compressed sensing is the extension of compressed sampling (CS) to sensor networks. The idea is to design a CS joint decoding scheme at a central decoder (base station) that exploits the inter-sensor correlations, in order to recover the whole observations from very few number of random measurements per node. In this paper, we focus on modeling the correlations and on the design and analysis of efficient joint recovery algorithms. We show, by extending earlier results of Baron et al.,1 that a simple thresholding algorithm can exploit the full diversity offered by all channels to identify a common sparse support using a near optimal number of measurements.

Average case analysis of sparse recovery with thresholding : New bounds based on average dictionary coherence

This paper analyzes the performance of the simple thresholding algorithm for sparse signal representations. In particular, in order to be more realistic we introduce a new probabilistic signal model which assumes randomness for both the amplitude and also the location of nonzero entries. Based on this model we show that thresholding in average can correctly recover signals for much higher sparsity levels than was previously reported. The bounds we obtain in this paper are based on a new concept of average dictionary coherence and are shown to be much sharper than in former works [1,2].

Insense: Incoherent Sensor Selection for Sparse Signals

Sensor selection refers to the problem of intelligently selecting a small subset of a collection of available sensors to reduce the sensing cost while preserving signal acquisition performance. The majority of sensor selection algorithms find the subset of sensors that best recovers an arbitrary signal from a number of linear measurements that is larger than the dimension of the signal. In this paper, we develop a new sensor selection algorithm for sparse (or near sparse) signals that finds a subset of sensors that best recovers such signals from a number of measurements that is much smaller than the dimension of the signal. Existing sensor selection algorithms cannot be applied in such situations. Our proposed Incoherent Sensor Selection (Insense) algorithm minimizes a coherence-based cost function that is adapted from recent results in sparse recovery theory. Using three datasets, including a real-world dataset on microbial diagnostics, we demonstrate the superior performance of Insense for sparse-signal sensor selection.