Ankita Shukla

Split Bregman algorithms for sparse / joint-sparse and low-rank signal recovery: Application in compressive hyperspectral imaging

In this work we derive algorithms for solving two problems - the first one is the combined l1-norm (sparsity) and nuclear norm (low rank) regularized least squares problem and the second one is the l2, 1-norm (joint sparsity) and nuclear norm regularized least squares problem. There are no efficient general purpose solvers for these problems; our work plugs this gap by deriving Split Bregman based algorithms for solving the said problems. Both algorithms are applicable for recovering hyperspectral images from their compressive measurements obtained via the single pixel camera. We show that our proposed techniques significantly outperform previous methods in terms of recovery accuracy.

Row-sparse blind compressed sensing for reconstructing multi-channel EEG signals

Abstract This communication concentrates on application of blind compressed sensing (BCS) framework for reconstruction of multichannel electroencephalograph (EEG) signal for wireless body area networks (WBANs). Compressed sensing (CS) based techniques employ a known sparsifying basis (wavelet/DCT/Gabor). BCS learns the sparsifying dictionary while recovering the signal. The BCS framework was proposed for recovering sparse signals. A recent work showed that, EEG signals can be better recovered by exploiting inter-channel correlation. This led to a row-sparse recovery problem. In this work, we modify the basic BCS framework for recovering row-sparse signal ensembles – this leads to better EEG reconstruction accuracy compared to prior CS recovery methods. The success of this technique enables reducing the energy expenditure of the sensor nodes of the WBAN.

Matrix Recovery Using Split Bregman

In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless sensor networks, control systems, recommender systems, image/video reconstruction etc. Both in theory and practice, the most optimal way to solve the low rank matrix recovery problem is via nuclear norm minimization. In this paper, we propose a Split Bregman algorithm for nuclear norm minimization. The use of Bregman technique improves the convergence speed of our algorithm and gives a higher success rate. Also, the accuracy of reconstruction is much better even for cases where small number of linear measurements are available. Our claim is supported by empirical results obtained using our algorithm and its comparison to other existing methods for matrix recovery. The algorithms are compared on the basis of NMSE, execution time and success rate for varying ranks and sampling ratios.

Energy efficient acquisition and reconstruction of EEG signals

In Wireless Body Area Networks (WBAN) the energy consumption is dominated by sensing and communication. Previous Compressed Sensing (CS) based solutions to EEG tele-monitoring over WBANs could only reduce the communication cost. In this work, we propose a matrix completion based formulation that can also reduce the energy consumption for sensing. We test our method with state-of-the-art CS based techniques and find that the reconstruction accuracy from our method is significantly better and that too at considerably less energy consumption. Our method is also tested for post-reconstruction signal classification where it outperforms previous CS based techniques. At the heart of the system is an Analog to Information Converter (AIC) implemented in 65nm CMOS technology. The pseudorandom clock generator enables random under-sampling and subsequent conversion by the 12-bit Successive Approximation Register Analog to Digital Converter (SAR ADC). AIC achieves a sample rate of 0.5 KS/s, an ENOB 9.54 bits, and consumes 108 nW from 1 V power supply.

Combining sparsity with rank-deficiency for energy efficient EEG sensing and transmission over Wireless Body Area Network

In Wireless Body Area Networks (WBAN) the energy consumption is dominated by sensing and communication. Previous techniques exploited the sparsity of the signal (in transform domains) to reduce communication costs for EEG transmission. For the first time, in this work, we propose to jointly exploit sparsity and rank-deficiency of the multi-channel signal ensemble in order to reduce both sensing and communication power consumptions. We test our method with state-of-the-art recovery techniques and find that the reconstruction accuracy from our method is considerably better and that too at lower energy consumption.

Exploiting inter-channel correlation in EEG signal reconstruction

Abstract We address the problem of sensing and transmitting EEG signals over wireless body area network (WBAN). Compressed sensing (CS) techniques are used profusely to this end. However, all prior techniques concentrate on piecemeal reconstruction of EEG signals from individual channels. For the first time, we show how inter-channel correlation can be exploited to achieve better reconstruction. We propose to model the multi-channel signal ensemble as (1) a low-rank matrix, (2) a row-sparse matrix (in transform domain) and (3) a combination of the two. Improved signal reconstruction is not the only goal of this work; our approach can also reduce the total energy requirement of the EEG sensor nodes by a significant amount. Prior techniques could only reduce transmission energy, but our method can reduce acquisition energy and eliminate the processing energy required for compression.

Real-Time Dynamic MRI Reconstruction: Accelerating Compressed Sensing on Graphical Processor Unit

The aim of this paper is to propose techniques for realtime dynamic MRI reconstruction from partially sampled K-space measurements. Previous techniques in this area are either fast but inaccurate or are slow (therefore not amenable for real-time reconstruction) but with higher degree of accuracy. Recently a Compressed Sensing based algorithm has been proposed which yields high degree of reconstruction accuracy at near real-time speeds. But any attempt to improve one (speed or accuracy) results in reduction of the other. In this work, we propose to improve speed and accuracy of the existing CS algorithm by parallelizing it on a Graphical Processing Unit (GPU). We see that our parallelized dynamic MRI reconstruction algorithm achieves real-time reconstruction speeds and improves the reconstruction accuracy at the same time.

A Kronecker Compressed Sensing formulation for energy efficient EEG sensing

In Wireless Body Area Networks (WBAN) the energy consumption is dominated by sensing, processing and communication. Previous Compressed Sensing (CS) based solutions to EEG tele-monitoring over WBANs could only reduce the communication cost. In this work, we propose to reduce the sensing and processing energy costs as well, by randomly under-sampling the signal. We formulate a theoretically sound framework based on Kronecker Compressed Sensing (KCS) for recovering signals acquired via random under-sampling. We have shown experimentally that when the signals are acquired via under-sampling, all previous CS based techniques fail; only our proposed formulation succeeds. We have also carried out a discussion on the power savings provided by our method; the analysis indicate significant reduction in energy cost.

Metric learning based automatic segmentation of patterned species

Many species in the wild exhibit a visual pattern that can be used to uniquely identify an individual. This observation has recently led to visual animal biometrics become a rapidly growing application area of computer vision. Customized software tools for animal biometrics already employ vision based techniques to recognize individuals in images taken in uncontrolled environments. However, most existing tools require the user to localize the animals for accurate identification. In this work, we propose a figure/ground segmentation method that automatically extracts out the animal in an image. Our method relies on a semi-supervised metric learning algorithm that uses a small amount of training data without compromising generalization performance. We design a simple pipeline comprising of superpixel segmentation, texture based feature extraction followed by mean shift clustering using the learned metric. We show that our approach can yield competitive results for figure/ground segmentation of patterned animals in images taken in the wild, often under extreme illumination conditions.

Distance Metric Learning by Optimization on the Stiefel Manifold

Distance metric learning has proven to be very successful in various problem domains. Most techniques learn a global metric in the form of a n× n symmetric positive semidefinite (PSD) Mahalanobis distance matrix, which has O(n2) unknowns. The PSD constraint makes solving the metric learning problem even harder making it computationally intractable for high dimensions. In this work, we propose a flexible formulation that can employ different regularization functions, while implicitly maintaining the positive semidefiniteness constraint. We achieve this by eigendecomposition of the rank p Mahalanobis distance matrix followed by a joint optimization on the Stiefel manifold Sn,p and the positive orthant R +. The resulting nonconvex optimization problem is solved by employing an alternating strategy. We use a recently proposed projection free approach for efficient optimization over the Stiefel manifold. Even though the problem is nonconvex, we empirically show competitive classification accuracy on UCI and USPS digits datasets.