Publications
255 results found
Murray-Bruce J, Dragotti PL, 2017, Solving Inverse Source Problems for linear PDEs using Sparse Sensor Measurements, 50th Asilomar Conference on Signals, Systems, and Computers (ASILOMARSSC), Publisher: IEEE, Pages: 517-521, ISSN: 1058-6393
Many physical phenomena across several applications can be described by partial differential equations (PDEs). In these applications, sensors collect sparse samples of the resulting phenomena with the aim of detecting its cause/source, using some intelligent data analysis tools on the samples. These problems are commonly referred to as inverse source problems. This work presents a novel framework for solving such inverse source problem for linear PDEs by drawing from certain recent results in modern sampling theory. Under the new framework, we study the well-known diffusion PDE and present numerical results that highlight the validity and robustness of the approach.
Huang J-J, Dragotti PL, 2017, PROSPARSE EXTENSION: PRONY'S BASED SPARSE PATTERN RECOVERY WITH EXTENDED DICTIONARIES, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 3819-3823, ISSN: 1520-6149
Wei X, Dragotti PL, 2017, MODEL ORDER SELECTION FOR SAMPLING FRI SIGNALS, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 4556-4560, ISSN: 1520-6149
Lawson M, Brookes M, Dragotti PL, 2017, IDENTIFYING A MULTIPLE PLANE PLENOPTIC FUNCTION FROM A SWIPED IMAGE, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 1423-1427, ISSN: 1520-6149
Dragotti P, Murray-Bruce M, 2016, Solving physics-driven inverse problems via structured least squares, EUSIPCO 2016, Publisher: IEEE, Pages: 331-335, ISSN: 2076-1465
Numerous physical phenomena are well modeled by partialdifferential equations (PDEs); they describe a wide range ofphenomena across many application domains, from model-ing EEG signals in electroencephalography to, modeling therelease and propagation of toxic substances in environmentalmonitoring. In these applications it is often of interest to findthe sources of the resulting phenomena, given some sparsesensor measurements of it. This will be the main task of thiswork. Specifically, we will show that finding the sources ofsuch PDE-driven fields can be turned into solving a class ofwell-known multi-dimensional structured least squares prob-lems. This link is achieved by leveraging from recent resultsin modern sampling theory – in particular, the approximateStrang-Fix theory. Subsequently, numerical simulation re-sults are provided in order to demonstrate the validity androbustness of the proposed framework.
Lawson M, Brookes M, Dragotti PL, 2016, Capturing the plenoptic function in a swipe, Conference on Applications of Digital Image Processing XXXIX, Publisher: Society of Photo-optical Instrumentation Engineers, ISSN: 0277-786X
Dragotti P, Wei X, 2016, FRESH – FRI-based single-image super-resolution algorithm, IEEE Transactions on Image Processing, Vol: 25, Pages: 3723-3735, ISSN: 1057-7149
In this paper, we consider the problem of single image super-resolution and propose a novel algorithm that outperforms state-of-the-art methods without the need of learning patches pairs from external data sets. We achieve this by modeling images and, more precisely, lines of images as piecewise smooth functions and propose a resolution enhancement method for this type of functions. The method makes use of the theory of sampling signals with finite rate of innovation (FRI) and combines it with traditional linear reconstruction methods. We combine the two reconstructions by leveraging from the multi-resolution analysis in wavelet theory and show how an FRI reconstruction and a linear reconstruction can be fused using filter banks. We then apply this method along vertical, horizontal, and diagonal directions in an image to obtain a single-image super-resolution algorithm. We also propose a further improvement of the method based on learning from the errors of our super-resolution result at lower resolution levels. Simulation results show that our method outperforms state-of-the-art algorithms under different blurring kernels.
Zhang Y, Dragotti P-L, 2016, Sampling streams of pulses with unknown shapes, IEEE Transactions on Signal Processing, Vol: 64, Pages: 5450-5465, ISSN: 1053-587X
This paper extends the class of continuous-time signals that can be perfectly reconstructed by developing a theory for the sampling and exact reconstruction of streams of short pulses with unknown shapes. The single pulse is modelled as the delayed version of a wavelet-sparse signal, which is normally not band limited. As the delay can be an arbitrary real number, it is hard to develop an exact sampling result for this type of signals. We achieve the exact reconstruction of the pulses by using only the knowledge of the Fourier transform of the signal at specific frequencies. We further introduce a multi-channel acquisition system which uses a new family of compact-support sampling kernels for extracting the Fourier information from the samples. The shape of the kernel is independent of the wavelet basis in which the pulse is sparse and hence the same acquisition system can be used with pulses which are sparse on different wavelet bases. By exploiting the fact that pulses have short duration and that the sampling kernels have compact support, we finally propose a local and sequential algorithm to reconstruct streaming pulses from the samples.
Reynolds S, Copeland CS, Schultz SR, et al., 2016, An extension of the FRI framework for calcium transient detection, IEEE 13th International Symposium on Biomedical Imaging (ISBI), Publisher: IEEE, Pages: 676-679, ISSN: 1945-7928
Two-photon calcium imaging of the brain allows the spatiotemporal activity of neuronal networks to be monitored at cellular resolution. In order to analyse this activity it must first be possible to detect, with high temporal resolution, spikes from the time series corresponding to single neurons. Previous work has shown that finite rate of innovation (FRI) theory can be used to reconstruct spike trains from noisy calcium imaging data. In this paper we extend the FRI framework for spike detection from calcium imaging data to encompass data generated by a larger class of calcium indicators, including the genetically encoded indicator GCaMP6s. Furthermore, we implement least squares model-order estimation and perform a noise reduction procedure ('pre-whitening') in order to increase the robustness of the algorithm. We demonstrate high spike detection performance on real data generated by GCaMP6s, detecting 90% of electrophysiologically-validated spikes.
Murray-Bruce J, Dragotti PL, 2016, Physics-driven quantized consensus for distributed diffusion source estimation using sensor networks, Eurasip Journal on Advances in Signal Processing, Vol: 2016, ISSN: 1687-6180
Sensor networks are important for monitoring several physical phenomena. In this paper, we consider the monitoring of diffusion fields and design simple, yet robust, sensing, data processing and communication strategies for estimating the sources of diffusion fields under communication constraints. Specifically, based on our previous work in the area, we firstly show how sources of the field can be recovered analytically through the use of well-chosen sensing functions. Then, by properly extending this scheme to our sensor network setting, we design and propose an effective diffusion field sensing strategy. Next, we introduce a physics-driven quantized gossip scheme, as a joint information processing and communication strategy for handling the network communication constraints: i.e. when a sensor can only communicate with a small subset of nodes over links with a finite capacity. Combining the proposed strategies allows us to develop a fully distributed algorithm for recovering sources of diffusion fields using sensor networks. Numerical simulation results are presented in order to evaluate the effectiveness and robustness of our algorithm.
Murray-Bruce J, Dragotti PL, 2016, RECONSTRUCTING NON-POINT SOURCES OF DIFFUSION FIELDS USING SENSOR MEASUREMENTS, 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE, Pages: 4004-4008, ISSN: 1520-6149
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- Citations: 1
Kotzagiannidis MS, Dragotti PL, 2016, THE GRAPH FRI FRAMEWORK-SPLINE WAVELET THEORY AND SAMPLING ON CIRCULANT GRAPHS, 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE, Pages: 6375-6379, ISSN: 1520-6149
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- Citations: 5
Onativia J, Lu YM, Dragotti PL, 2016, PROSPARSE DENOISE: PRONY'S BASED SPARSE PATTERN RECOVERY IN THE PRESENCE OF NOISE, 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE, Pages: 4084-4088, ISSN: 1520-6149
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- Citations: 2
Maggioni M, Dragotti PL, 2016, Video Temporal Super-Resolution Using Nonlocal Registration and Self-Similarity, 18th IEEE International Workshop on Multimedia Signal Processing (MMSP), Publisher: IEEE, ISSN: 2163-3517
Tagliasacchi M, Visentini-Scarzanella M, Dragotti PL, et al., 2015, Identification of transform coding chains, IEEE Transactions on Image Processing, Vol: 25, Pages: 1109-1123, ISSN: 1941-0042
Wei X, Dragotti PL, 2015, Guaranteed performance in the FRI setting, IEEE Signal Processing Letters, Vol: 22, Pages: 1661-1665, ISSN: 1558-2361
Finite Rate of Innovation (FRI) sampling theory has shown that it is possible to sample and perfectly reconstruct classes of non-bandlimited signals such as streams of Diracs. In the case of noisy measurements, FRI methods achieve the optimal performance given by the Cramér-Rao bound up to a certain PSNR and breaks down for smaller PSNRs. To the best of our knowledge, the precise anticipation of the breakdown event in FRI settings is still an open problem. In this letter, we address this issue by investigating the subspace swap event which has been broadly recognised as the reason for performance breakdown in SVD-based parameter estimation algorithms. We work out at which noise level the absence of subspace swap is guaranteed and this gives us an accurate prediction of the breakdown PSNR which we also relate to the sampling rate and the distance between adjacent Diracs. Simulation results validate the reliability of our analysis.
Zhang Y, Dragotti PL, 2015, On the Reconstruction of Wavelet-Sparse Signals From Partial Fourier Information, IEEE SIGNAL PROCESSING LETTERS, Vol: 22, Pages: 1234-1238, ISSN: 1070-9908
Murray-Bruce J, Dragotti PL, 2015, Estimating localized sources of diffusion fields using spatiotemporal sensor measurements, IEEE Transactions on Signal Processing, Vol: 63, Pages: 3018-3031, ISSN: 1053-587X
We consider diffusion fields induced by a finite number of spatially localized sources and address the problem of estimating these sources using spatiotemporal samples of the field obtained with a sensor network. Within this framework, we consider two different time evolutions: the case where the sources are instantaneous, as well as, the case where the sources decay exponentially in time after activation. We first derive novel exact inversion formulas, for both source distributions, through the use of Green's second theorem and a family of sensing functions to compute generalized field samples. These generalized samples can then be inverted using variations of existing algebraic methods such as Prony's method. Next, we develop a novel and robust reconstruction method for diffusion fields by properly extending these formulas to operate on the spatiotemporal samples of the field. Finally, we present numerical results using both synthetic and real data to verify the algorithms proposed herein.
Thongkamwitoon T, Muammar H, Dragotti P-L, 2015, An image recapture detection algorithm based on learning dictionaries of edge profiles, IEEE Transactions on Information Forensics and Security, Vol: 10, Pages: 953-968, ISSN: 1556-6013
With today's digital camera technology, high-quality images can be recaptured from an liquid crystal display (LCD) monitor screen with relative ease. An attacker may choose to recapture a forged image in order to conceal imperfections and to increase its authenticity. In this paper, we address the problem of detecting images recaptured from LCD monitors. We provide a comprehensive overview of the traces found in recaptured images, and we argue that aliasing and blurriness are the least scene dependent features. We then show how aliasing can be eliminated by setting the capture parameters to predetermined values. Driven by this finding, we propose a recapture detection algorithm based on learned edge blurriness. Two sets of dictionaries are trained using the K-singular value decomposition approach from the line spread profiles of selected edges from single captured and recaptured images. An support vector machine classifier is then built using dictionary approximation errors and the mean edge spread width from the training images. The algorithm, which requires no user intervention, was tested on a database that included more than 2500 high-quality recaptured images. Our results show that our method achieves a performance rate that exceeds 99% for recaptured images and 94% for single captured images.
Onativia J, Lu YM, Dragotti PL, 2015, SPARSITY PATTERN RECOVERY USING FRI METHODS, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 5967-5971, ISSN: 1520-6149
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- Citations: 1
Murray-Bruce J, Dragotti PL, 2015, CONSENSUS FOR THE DISTRIBUTED ESTIMATION OF POINT DIFFUSION SOURCES IN SENSOR NETWORKS, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 3262-3266, ISSN: 1520-6149
Murray-Bruce J, Dragotti PL, 2015, CONSENSUS FOR THE DISTRIBUTED ESTIMATION OF POINT DIFFUSION SOURCES IN SENSOR NETWORKS, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 3262-3266, ISSN: 1520-6149
Reynolds S, Onativia J, Copeland CS, et al., 2015, Spike Detection Using FRI Methods and Protein Calcium Sensors: Performance Analysis and Comparisons, International Conference on Sampling Theory and Applications (SampTA), Publisher: IEEE, Pages: 533-537
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- Citations: 4
Wei X, Dragotti PL, 2015, SAMPLING PIECEWISE SMOOTH SIGNALS AND ITS APPLICATION TO IMAGE UP-SAMPLING, IEEE International Conference on Image Processing (ICIP), Publisher: IEEE, Pages: 4293-4297, ISSN: 1522-4880
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- Citations: 5
Onativia J, Lu YM, Dragotti PL, 2015, SPARSITY PATTERN RECOVERY USING FRI METHODS, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 5967-5971, ISSN: 1520-6149
- Author Web Link
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- Citations: 1
Kotzagiannidis MS, Dragotti PL, 2015, Higher-order graph wavelets and sparsity on circulant graphs, Conference on Wavelets and Sparsity XVI, Publisher: SPIE-INT SOC OPTICAL ENGINEERING, ISSN: 0277-786X
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- Citations: 2
Onativia J, Dragotti PL, 2014, Sparse sampling: theory, methods and an application in neuroscience, Biological Cybernetics, Vol: 109, Pages: 125-139, ISSN: 1432-0770
Dragotti PL, Lu YM, 2014, On sparse representation in Fourier and local bases, IEEE Transactions on Information Theory, Vol: 60, Pages: 7888-7899, ISSN: 0018-9448
We consider the classical problem of finding the sparse representation of a signal in a pair of bases. When both bases are orthogonal, it is known that the sparse representation is unique when the sparsity K of the signal satisfies K <; 1/μ(D), where μ(D) is the mutual coherence of the dictionary. Furthermore, the sparse representation can be obtained in polynomial time by basis pursuit (BP), when K <; 0.91/μ(D). Therefore, there is a gap between the unicity condition and the one required to use the polynomial-complexity BP formulation. For the case of general dictionaries, it is also well known that finding the sparse representation under the only constraint of unicity is NP-hard. In this paper, we introduce, for the case of Fourier and canonical bases, a polynomial complexity algorithm that finds all the possible K-sparse representations of a signal under the weaker condition that K <; √2/μ(D). Consequently, when K <; 1/μ(D), the proposed algorithm solves the unique sparse representation problem for this structured dictionary in polynomial time. We further show that the same method can be extended to many other pairs of bases, one of which must have local atoms. Examples include the union of Fourier and local Fourier bases, the union of discrete cosine transform and canonical bases, and the union of random Gaussian and canonical bases.
Dragotti P, scholefield, 2014, AccurateiImage registration using approximate Strang-Fix and an application in image super-resolution, EUSIPCO, Publisher: IEEE, ISSN: 2076-1465
Accurate registration is critical to most multi-channel signal processing setups, including image super-resolution. In this paper we use modern sampling theory to propose a new robust registration algorithm that works with arbitrary sampling kernels. The algorithm accurately approximates continuous-time Fourier coefficients from discrete-time samples. These Fourier coefficients can be used to construct an over-complete system, which can be solved to approximate translational motion at around 100-th of a pixel accuracy. The over-completeness of the system provides robustness to noise and other modelling errors. For example we show an image registration result for images that have slightly different backgrounds, due to a viewpoint translation. Our previous registration techniques, based on similar sampling theory, can provide a similar accuracy but not under these more general conditions. Simulation results demonstrate the accuracy and robustness of the approach and demonstrate the potential applications in image super-resolution.
Murray-Bruce J, Dragotti PL, 2014, Reconstructing diffusion fields sampled with a network of arbitrarily distributed sensors, Signal Processing Conference (EUSIPCO) 2014, Publisher: IEEE, Pages: 885-889, ISSN: 2219-5491
Sensor networks are becoming increasingly prevalent for monitoring physical phenomena of interest. For such wireless sensor network applications, knowledge of node location is important. Although a uniform sensor distribution is common in the literature, it is normally difficult to achieve in reality. Thus we propose a robust algorithm for reconstructing two-dimensional diffusion fields, sampled with a network of arbitrarily placed sensors. The two-step method proposed here is based on source parameter estimation: in the first step, by properly combining the field sensed through well-chosen test functions, we show how Prony's method can reveal locations and intensities of the sources inducing the field. The second step then uses a modification of the Cauchy-Schwarz inequality to estimate the activation time in the single source field. We combine these steps to give a multi-source field estimation algorithm and carry out extensive numerical simulations to evaluate its performance.
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