Compressively Sensed Image Recognition

Compressive Sensing (CS) theory asserts that sparse signal reconstruction is possible from a small number of linear measurements. Although CS enables low-cost linear sampling, it requires non-linear and costly reconstruction. Recent literature works show that compressive image classification is possible in CS domain without reconstruction of the signal. In this work, we introduce a DCT base method that extracts binary discriminative features directly from CS measurements. These CS measurements can be obtained by using (i) a random or a pseudo-random measurement matrix, or (ii) a measurement matrix whose elements are learned from the training data to optimize the given classification task. We further introduce feature fusion by concatenating Bag of Words (BoW) representation of our binary features with one of the two state-of-the-art CNN-based feature vectors. We show that our fused feature outperforms the state-of-the-art in both cases.Comment: 6 pages, submitted/accepted, EUVIP 201

Granger Causality for Compressively Sensed Sparse Signals

Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted and stored using far fewer measurements than done by conventional means employing Nyquist sampling theorem. Since many naturally occurring signals are sparse (in some domain), compressed sensing has rapidly seen popularity in a number of applied physics and engineering applications, particularly in designing signal and image acquisition strategies, e.g., magnetic resonance imaging, quantum state tomography, scanning tunneling microscopy, analog to digital conversion technologies. Contemporaneously, causal inference has become an important tool for the analysis and understanding of processes and their interactions in many disciplines of science, especially those dealing with complex systems. Direct causal analysis for compressively sensed data is required to avoid the task of reconstructing the compressed data. Also, for some sparse signals, such as for sparse temporal data, it may be difficult to discover causal relations directly using available data-driven/ model-free causality estimation techniques. In this work, we provide a mathematical proof that structured compressed sensing matrices, specifically Circulant and Toeplitz, preserve causal relationships in the compressed signal domain, as measured by Granger Causality. We then verify this theorem on a number of bivariate and multivariate coupled sparse signal simulations which are compressed using these matrices. We also demonstrate a real world application of network causal connectivity estimation from sparse neural spike train recordings from rat prefrontal cortex.Comment: Submitted to IEEE Transactions on Neural Networks and Learning System

Event-triggered state observers for sparse sensor noise/attacks

This paper describes two algorithms for state reconstruction from sensor measurements that are corrupted with sparse, but otherwise arbitrary, 'noise.' These results are motivated by the need to secure cyber-physical systems against a malicious adversary that can arbitrarily corrupt sensor measurements. The first algorithm reconstructs the state from a batch of sensor measurements while the second algorithm is able to incorporate new measurements as they become available, in the spirit of a Luenberger observer. A distinguishing point of these algorithms is the use of event-triggered techniques to improve the computational performance of the proposed algorithms

Performance Gains in Conjugate Gradient Computation with Linearly Connected GPU Multiprocessors

Conjugate gradient is an important iterative method used for solving least squares problems. It is compute-bound and generally involves only simple matrix computations. One would expect that we could fully parallelize such computation on the GPU architecture with multiple Stream Multiprocessors (SMs), each consisting of many SIMD processing units. While implementing a conjugate gradient method for compressive sensing signal reconstruction, we have noticed that large speed-up due to parallel processing is actually infeasible due to the high I/O cost between SMs and GPU global memory. WE have found that if SMs were linearly connected, we could gain a 15x speedup by loop unrolling. We conclude that adding these relatively inexpensive neighbor connections for SMs can significantly enhance the applicability of GPUs to a large class of similar matrix computations.Engineering and Applied Science

Convolutional Sparse Support Estimator Based Covid-19 Recognition from X-ray Images

Coronavirus disease (Covid-19) has been the main agenda of the whole world since it came in sight in December 2019. It has already caused thousands of causalities and infected several millions worldwide. Any technological tool that can be provided to healthcare practitioners to save time, effort, and possibly lives has crucial importance. The main tools practitioners currently use to diagnose Covid-19 are Reverse Transcription-Polymerase Chain reaction (RT-PCR) and Computed Tomography (CT), which require significant time, resources and acknowledged experts. X-ray imaging is a common and easily accessible tool that has great potential for Covid-19 diagnosis. In this study, we propose a novel approach for Covid-19 recognition from chest X-ray images. Despite the importance of the problem, recent studies in this domain produced not so satisfactory results due to the limited datasets available for training. Recall that Deep Learning techniques can generally provide state-of-the-art performance in many classification tasks when trained properly over large datasets, such data scarcity can be a crucial obstacle when using them for Covid-19 detection. Alternative approaches such as representation-based classification (collaborative or sparse representation) might provide satisfactory performance with limited size datasets, but they generally fall short in performance or speed compared to Machine Learning methods. To address this deficiency, Convolution Support Estimation Network (CSEN) has recently been proposed as a bridge between model-based and Deep Learning approaches by providing a non-iterative real-time mapping from query sample to ideally sparse representation coefficient' support, which is critical information for class decision in representation based techniques.Comment: 10 page

Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections

In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a reduced set of multi-way compressive measurements by exploiting its low multilinear-rank structure. Moreover, we show that, an interesting property of multi-way measurements allows us to build the reconstruction based on compressive linear measurements taken only in two selected modes, independently of the tensor order $N$. In addition, it is proved that, in the matrix case and in a particular case with $3$rd-order tensors where the same 2D sensor operator is applied to all mode-3 slices, the proposed reconstruction $\underline{\mathbf{X}}_\tau$ is stable in the sense that the approximation error is comparable to the one provided by the best low-multilinear-rank approximation, where $\tau$ is a threshold parameter that controls the approximation error. Through the analysis of the upper bound of the approximation error we show that, in the 2D case, an optimal value for the threshold parameter $\tau=\tau_0 > 0$ exists, which is confirmed by our simulation results. On the other hand, our experiments on 3D datasets show that very good reconstructions are obtained using $\tau=0$, which means that this parameter does not need to be tuned. Our extensive simulation results demonstrate the stability and robustness of the method when it is applied to real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity based CS methods specialized for multidimensional signals is also included. A very attractive characteristic of the proposed method is that it provides a direct computation, i.e. it is non-iterative in contrast to all existing sparsity based CS algorithms, thus providing super fast computations, even for large datasets.Comment: Submitted to IEEE Transactions on Signal Processin

Computer Vision from Spatial-Multiplexing Cameras at Low Measurement Rates

abstract: In UAVs and parking lots, it is typical to first collect an enormous number of pixels using conventional imagers. This is followed by employment of expensive methods to compress by throwing away redundant data. Subsequently, the compressed data is transmitted to a ground station. The past decade has seen the emergence of novel imagers called spatial-multiplexing cameras, which offer compression at the sensing level itself by providing an arbitrary linear measurements of the scene instead of pixel-based sampling. In this dissertation, I discuss various approaches for effective information extraction from spatial-multiplexing measurements and present the trade-offs between reliability of the performance and computational/storage load of the system. In the first part, I present a reconstruction-free approach to high-level inference in computer vision, wherein I consider the specific case of activity analysis, and show that using correlation filters, one can perform effective action recognition and localization directly from a class of spatial-multiplexing cameras, called compressive cameras, even at very low measurement rates of 1\%. In the second part, I outline a deep learning based non-iterative and real-time algorithm to reconstruct images from compressively sensed (CS) measurements, which can outperform the traditional iterative CS reconstruction algorithms in terms of reconstruction quality and time complexity, especially at low measurement rates. To overcome the limitations of compressive cameras, which are operated with random measurements and not particularly tuned to any task, in the third part of the dissertation, I propose a method to design spatial-multiplexing measurements, which are tuned to facilitate the easy extraction of features that are useful in computer vision tasks like object tracking. The work presented in the dissertation provides sufficient evidence to high-level inference in computer vision at extremely low measurement rates, and hence allows us to think about the possibility of revamping the current day computer systems.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201