Browsing by Subject "Compressive sensing"

Now showing 1 - 20 of 32

Open Access
Average error in recovery of sparse signals and discrete fourier transform
(IEEE, 2012-04) Özçelikkale, Ayça; Yüksel, S.; Özaktaş Haldun M.
In compressive sensing framework it has been shown that a sparse signal can be successfully recovered from a few random measurements. The Discrete Fourier Transform (DFT) is one of the transforms that provide the best performance guarantees regardless of which components of the signal are nonzero. This result is based on the performance criterion of signal recovery with high probability. Whether the DFT is the optimum transform under average error criterion, instead of high probability criterion, has not been investigated. Here we consider this optimization problem. For this purpose, we model the signal as a random process, and propose a model where the covariance matrix of the signal is used as a measure of sparsity. We show that the DFT is, in general, not optimal despite numerous results that suggest otherwise. © 2012 IEEE.
Open Access
Coded scenes for fast system calibration in magnetic particle imaging
(IEEE, 2018) Ilbey, S.; Top, C. B.; Güngör, A.; Sarıtaş, Emine Ülkü; Güven, E.
Magnetic nanoparticle (MNP) agents have a wide range of clinical application areas for both imaging and therapy. MNP distribution inside the body can be imaged using Magnetic Particle Imaging (MPI). For MPI image reconstruction with the system function matrix (SFM) approach, a calibration scan is necessary, in which a single MNP sample is placed and scanned inside the full field of view (FOV), which is a very time consuming task. In this study, we propose the use of coded scenes that include MNP samples at multiple positions inside the FOV, and reconstruct the SFM using compressed sensing techniques. We used simulations to analyze the effect of number of coded scenes on the image quality, and compare the results with standard sparse reconstruction using single MNP sample scan. The results show that with the proposed method, the required number of measurements is decreased substantially, enabling a fast system calibration procedure.
Open Access
A compression method based on compressive sampling for 3-D laser range scans of indoor environments
(Springer, Dordrecht, 2010) Dobrucalı, Oğuzcan; Barshan, Billur
When 3-D models of environments need to be transmitted or stored, they should be compressed efficiently to increase the capacity of the communication channel or the storage medium. We propose a novel compression technique based on compressive sensing, applied to sparse representations of 3-D range measurements. We develop a novel algorithm to generate sparse innovations between consecutive range measurements along the axis of the sensor's motion, since the range measurements do not have highly sparse representations in common domains. Compared with the performances of widely used compression techniques, the proposed method offers the smallest compression ratio and provides a reasonable balance between reconstruction error and processing time. © 2011 Springer Science+Business Media B.V.
Open Access
A compression method for 3-D laser range scans of indoor environments based on compressive sensing
(IEEE, 2011-08-09) Dobrucalı, Oğuzcan; Barshan, Biilur
Modeling and representing 3-D environments require the transmission and storage of vast amount of measurements that need to be compressed efficiently. We propose a novel compression technique based on compressive sensing for 3-D range measurements that are found to be correlated with each other. The main issue here is finding a highly sparse representation of the range measurements, since they do not have highly sparse representations in common domains, such as the frequency domain. To solve this problem, we generate sparse innovations between consecutive range measurements along the axis of the sensor's motion. We obtain highly sparse innovations compared with other possible ones generated by estimation and filtering. Being a lossy technique, the proposed method performs reasonably well compared with widely used compression techniques. © 2011 EURASIP.
Open Access
Compressive digital receiver: first results on sensitivity, dynamic range and instantaneous bandwidth measurements
(Institute of Electrical and Electronics Engineers Inc., 2019) Korucu, A. B.; Alp, Y. K.; Gök, G.; Arıkan, Orhan
In this work, sensitivity, one/two-signal dynamic range and instantaneous bandwidth measurement results of the recently developed Compressive Digital Receiver (CDR) hardware for Electronic Support Measures (ESM) applications, will be reported for the first time. Developed CDR is a compressive sensing based sub-Nyquist sampling receiver, which can monitor 2.25 GHz bandwidth instantaneously by using four ADCs (Analog-to-Digital Receiver) each of which has a sampling rate of 250 MHz. All the digital processing blocks of the CDR are implemented in Field Programmable Gate Array (FPGA) and they work in real time. It is observed that the sensitivity and dynamic range of the CDR changes with respect to input signal frequency. For 2.25 GHz bandwidth, the best and worst sensitivity values of the CDR are reported as -62 dBm and -41 dBm, respectively. One-signal dynamic range of CDR is measured as at least 60 dB for the whole band. The best and worst values of the two-signal dynamic rage values are observed as 42 dB and 20 dB, respectively.
Open Access
Compressive sensing based flame detection in infrared videos
(IEEE, 2013) Günay, Osman; Çetin, A. Enis
In this paper, a Compressive Sensing based feature extraction algorithm is proposed for flame detection using infrared cameras. First, bright and moving regions in videos are detected. Then the videos are divided into spatio-temporal blocks and spatial and temporal feature vectors are exctracted from these blocks. Compressive Sensing is used to exctract spatial feature vectors. Compressed measurements are obtained by multiplying the pixels in the block with the sensing matrix. A new method is also developed to generate the sensing matrix. A random vector generated according to standard Gaussian distribution is passed through a wavelet transform and the resulting matrix is used as the sensing matrix. Temporal features are obtained from the vector that is formed from the difference of mean intensity values of the frames in two neighboring blocks. Spatial feature vectors are classified using Adaboost. Temporal feature vectors are classified using hidden Markov models. To reduce the computational cost only moving and bright regions are classified and classification is performed at specified intervals instead of every frame. © 2013 IEEE.
Open Access
Compressive sensing based target detection in delay-doppler radars
(IEEE, 2013) Teke, Oguzhan; Arıkan, Orhan; Gürbüz, A.C.
Compressive Sensing theory shows that, a sparse signal can be reconstructed from its sub-Nyquist rate random samples. With this property, CS approach has many applications. Radar systems, which deal with sparse signal due to its nature, is one of the important application of CS theory. Even if CS approach is suitable for radar systems, classical detections schemes under Neyman-Pearson formulations may result high probability of false alarm, when CS approach is used, especially if the target has off-grid parameters. In this study, a new detection scheme which enables CS techniques to be used in radar systems is investigated. © 2013 IEEE.
Open Access
Compressive sensing imaging with a graphene modulator at THz frequency in transmission mode
(IEEE, 2016) Özkan, V. A.; Takan, T.; Kakenov, Nurbek; Kocabaş, Coşkun; Altan, H.
In this study we demonstrate compressive sensing imaging with a unique graphene based optoelectronic device which allows us to modulate the THz field through an array of columns or rows distributed throughout its face.
Open Access
Compressive sensing-based robust off-the-grid stretch processing
(Institution of Engineering and Technology, 2017) Ilhan, I.; Gurbuz, A. C.; Arıkan, Orhan
Classical stretch processing (SP) obtains high range resolution by compressing large bandwidth signals with narrowband receivers using lower rate analogue-to-digital converters. SP achieves the resolution of the large bandwidth signal by focusing into a limited range window, and by deramping in the analogue domain. SP offers moderate data rate for signal processing for high bandwidth waveforms. Furthermore, if the scene in the examined window is sparse, compressive sensing (CS)-based techniques have the potential to further decrease the required number of measurements. However, CS-based reconstructions are highly affected by model mismatches such as targets that are off-the-grid. This study proposes a sparsity-based iterative parameter perturbation technique for SP that is robust to targets off-the-grid in range or Doppler. The error between reconstructed and actual scenes is measured using Earth mover's distance metric. Performance analyses of the proposed technique are compared with classical CS and SP techniques in terms of data rate, resolution and signal-to-noise ratio. It is shown through simulations that the proposed technique offers robust and high-resolution reconstructions for the same data rate compared with both classical SP- and CS-based techniques.
Open Access
Detection of sparse targets with structurally perturbed echo dictionaries
(Elsevier, 2013) Guldogan, M. B.; Arıkan, Orhan
In this paper, a novel algorithm is proposed to achieve robust high resolution detection in sparse multipath channels. Currently used sparse reconstruction techniques are not immediately applicable in multipath channel modeling. Performance of standard compressed sensing formulations based on discretization of the multipath channel parameter space degrade significantly when the actual channel parameters deviate from the assumed discrete set of values. To alleviate this off-grid problem, we make use of the particle swarm optimization (PSO) to perturb each grid point that reside in each multipath component cluster. Orthogonal matching pursuit (OMP) is used to reconstruct sparse multipath components in a greedy fashion. Extensive simulation results quantify the performance gain and robustness obtained by the proposed algorithm against the off-grid problem faced in sparse multipath channels.
Open Access
Expectation maximization based matching pursuit
(IEEE, 2012) Gurbuz, A.C.; Pilanci, M.; Arıkan, Orhan
A novel expectation maximization based matching pursuit (EMMP) algorithm is presented. The method uses the measurements as the incomplete data and obtain the complete data which corresponds to the sparse solution using an iterative EM based framework. In standard greedy methods such as matching pursuit or orthogonal matching pursuit a selected atom can not be changed during the course of the algorithm even if the signal doesn't have a support on that atom. The proposed EMMP algorithm is also flexible in that sense. The results show that the proposed method has lower reconstruction errors compared to other greedy algorithms using the same conditions. © 2012 IEEE.
Open Access
Learning-based compressive MRI
(Institute of Electrical and Electronics Engineers, 2018) Gözcü, B.; Mahabadi, R. K.; Li, Y. H.; Ilıcak, E.; Çukur, Tolga; Scarlett, J.; Cevher, V.
In the area of magnetic resonance imaging (MRI), an extensive range of non-linear reconstruction algorithms has been proposed which can be used with general Fourier subsampling patterns. However, the design of these subsampling patterns has typically been considered in isolation from the reconstruction rule and the anatomy under consideration. In this paper, we propose a learning-based framework for optimizing MRI subsampling patterns for a specific reconstruction rule and anatomy, considering both the noiseless and noisy settings. Our learning algorithm has access to a representative set of training signals, and searches for a sampling pattern that performs well on average for the signals in this set. We present a novel parameter-free greedy mask selection method and show it to be effective for a variety of reconstruction rules and performance metrics. Moreover, we also support our numerical findings by providing a rigorous justification of our framework via statistical learning theory.
Open Access
A new OMP technique for sparse recovery
(IEEE, 2012) Teke, Oğuzhan; Gürbüz, A.C.; Arıkan, Orhan
Compressive Sensing (CS) theory details how a sparsely represented signal in a known basis can be reconstructed using less number of measurements. However in reality there is a mismatch between the assumed and the actual bases due to several reasons like discritization of the parameter space or model errors. Due to this mismatch, a sparse signal in the actual basis is definitely not sparse in the assumed basis and current sparse reconstruction algorithms suffer performance degradation. This paper presents a novel orthogonal matching pursuit algorithm that has a controlled perturbation mechanism on the basis vectors, decreasing the residual norm at each iteration. Superior performance of the proposed technique is shown in detailed simulations. © 2012 IEEE.
Open Access
Online calibration of modulated wideband converter
(IEEE, 2016) Alp, Y. K.; Korucu, A. B.; Karabacak, A. T.; Gürbüz, A. C.; Arıkan, Orhan
In this work, we propose a new method for online calibration of recently proposed Modulated Wideband Converter (MWC), which digitizes wideband sparse signals below the Nyquist limit without loss of information by using compressive sensing techniques. Our method requires a single frequency synthesizer card, which can generate clean tones along the operation band of the system, rather than much expensive measurement instruments such as network analyser or vector spectrum analyser, which are not appropriate for online calibration. Moreover, low computational complexity of the proposed method enables its implementation on FPGA so that it can be embedded into the system. Hence, on each power on, the system can utilize self calibration without requiring any additional measurement instruments.
Open Access
Perturbed orthogonal matching pursuit
(IEEE, 2013) Teke, O.; Gurbuz, A. C.; Arıkan, Orhan
Compressive Sensing theory details how a sparsely represented signal in a known basis can be reconstructed with an underdetermined linear measurement model. However, in reality there is a mismatch between the assumed and the actual bases due to factors such as discretization of the parameter space defining basis components, sampling jitter in A/D conversion, and model errors. Due to this mismatch, a signal may not be sparse in the assumed basis, which causes significant performance degradation in sparse reconstruction algorithms. To eliminate the mismatch problem, this paper presents a novel perturbed orthogonal matching pursuit (POMP) algorithm that performs controlled perturbation of selected support vectors to decrease the orthogonal residual at each iteration. Based on detailed mathematical analysis, conditions for successful reconstruction are derived. Simulations show that robust results with much smaller reconstruction errors in the case of perturbed bases can be obtained as compared to standard sparse reconstruction techniques.
Open Access
Projections onto convex sets (POCS) based optimization by lifting
(IEEE, 2013) Çetin, A. Enis; Bozkurt, Alican; Günay, Osman; Habiboglu, Yusuf Hakan; Köse, K.; Onaran, İbrahim; Tofighi, Mohammad; Sevimli, Rasim Akın
A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in R N+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p < 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems. © 2013 IEEE.
Open Access
Range-doppler radar target detection using denoising within the compressive sensing framework
(IEEE, 2014-09) Sevimli, R. Akın; Tofighi, Mohammad; Çetin, A. Enis
Compressive sensing (CS) idea enables the reconstruction of a sparse signal from a small set of measurements. CS approach has applications in many practical areas. One of the areas is radar systems. In this article, the radar ambiguity function is denoised within the CS framework. A new denoising method on the projection onto the epigraph set of the convex function is also developed for this purpose. This approach is compared to the other CS reconstruction algorithms. Experimental results are presented1. © 2014 EURASIP.
Open Access
A recursive way for sparse reconstruction of parametric spaces
(IEEE, 2015-11) Teke, Oğuzhan; Gürbüz, A. C.; Arıkan, Orhan
A novel recursive framework for sparse reconstruction of continuous parameter spaces is proposed by adaptive partitioning and discretization of the parameter space together with expectation maximization type iterations. Any sparse solver or reconstruction technique can be used within the proposed recursive framework. Experimental results show that proposed technique improves the parameter estimation performance of classical sparse solvers while achieving Cramér-Rao lower bound on the tested frequency estimation problem. © 2014 IEEE.
Open Access
A robust compressive sensing based technique for reconstruction of sparse radar scenes
(Academic Press, 2014) Teke, O.; Gurbuz, A. C.; Arıkan, Orhan
Pulse-Doppler radar has been successfully applied to surveillance and tracking of both moving and stationary targets. For efficient processing of radar returns, delay-Doppler plane is discretized and FFT techniques are employed to compute matched filter output on this discrete grid. However, for targets whose delay-Doppler values do not coincide with the computation grid, the detection performance degrades considerably. Especially for detecting strong and closely spaced targets this causes miss detections and false alarms. This phenomena is known as the off-grid problem. Although compressive sensing based techniques provide sparse and high resolution results at sub-Nyquist sampling rates, straightforward application of these techniques is significantly more sensitive to the off-grid problem. Here a novel parameter perturbation based sparse reconstruction technique is proposed for robust delay-Doppler radar processing even under the off-grid case. Although the perturbation idea is general and can be implemented in association with other greedy techniques, presently it is used within an orthogonal matching pursuit (OMP) framework. In the proposed technique, the selected dictionary parameters are perturbed towards directions to decrease the orthogonal residual norm. The obtained results show that accurate and sparse reconstructions can be obtained for off-grid multi target cases. A new performance metric based on Kullback-Leibler Divergence (KLD) is proposed to better characterize the error between actual and reconstructed parameter spaces. Increased performance with lower reconstruction errors are obtained for all the tested performance criteria for the proposed technique compared to conventional OMP and ℓ1 minimization techniques. © 2013 Elsevier Inc.
Open Access
SAR image reconstruction and autofocus by compressed sensing
(Elsevier, 2012-07-24) Ugur, S.; Arıkan, Orhan
A new SAR signal processing technique based on compressed sensing is proposed for autofocused image reconstruction on subsampled raw SAR data. It is shown that, if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. To further improve image quality, the total variation of the reconstruction is used as a penalty term. In order to demonstrate the performance of the proposed technique in wide-band SAR systems, the measurements used in the reconstruction are formed by a new under-sampling pattern that can be easily implemented in practice by using slower rate A/D converters. Under a variety of metrics for the reconstruction quality, it is demonstrated that, even at high under-sampling ratios, the proposed technique provides reconstruction quality comparable to that obtained by the classical techniques which require full-band data without any under-sampling.