Extended object reconstruction in adaptive-optics imaging: the multiresolution approach

We propose the application of multiresolution transforms, such as wavelets (WT) and curvelets (CT), to the reconstruction of images of extended objects that have been acquired with adaptive optics (AO) systems. Such multichannel approaches normally make use of probabilistic tools in order to distinguish significant structures from noise and reconstruction residuals. Furthermore, we aim to check the historical assumption that image-reconstruction algorithms using static PSFs are not suitable for AO imaging. We convolve an image of Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m Hale telescope at the Palomar Observatory and add both shot and readout noise. Subsequently, we apply different approaches to the blurred and noisy data in order to recover the original object. The approaches include multi-frame blind deconvolution (with the algorithm IDAC), myopic deconvolution with regularization (with MISTRAL) and wavelets- or curvelets-based static PSF deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error (MSE) and the structural similarity index (SSIM) to compare the results. We discuss the strengths and weaknesses of the two metrics. We found that CT produces better results than WT, as measured in terms of MSE and SSIM. Multichannel deconvolution with a static PSF produces results which are generally better than the results obtained with the myopic/blind approaches (for the images we tested) thus showing that the ability of a method to suppress the noise and to track the underlying iterative process is just as critical as the capability of the myopic/blind approaches to update the PSF.Comment: In revision in Astronomy & Astrophysics. 19 pages, 13 figure

Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acoustic from the unknown competing speech sources relying on localization of the early images of the speakers by sparse approximation of the spatial spectra of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings demonstrate the effectiveness of the proposed approach for multi-party speech recovery and recognition.Comment: 31 page

Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution.Comment: 5 page

Multibaseline gravitational wave radiometry

We present a statistic for the detection of stochastic gravitational wave backgrounds (SGWBs) using radiometry with a network of multiple baselines. We also quantitatively compare the sensitivities of existing baselines and their network to SGWBs. We assess how the measurement accuracy of signal parameters, e.g., the sky position of a localized source, can improve when using a network of baselines, as compared to any of the single participating baselines. The search statistic itself is derived from the likelihood ratio of the cross correlation of the data across all possible baselines in a detector network and is optimal in Gaussian noise. Specifically, it is the likelihood ratio maximized over the strength of the SGWB, and is called the maximized-likelihood ratio (MLR). One of the main advantages of using the MLR over past search strategies for inferring the presence or absence of a signal is that the former does not require the deconvolution of the cross correlation statistic. Therefore, it does not suffer from errors inherent to the deconvolution procedure and is especially useful for detecting weak sources. In the limit of a single baseline, it reduces to the detection statistic studied by Ballmer [Class. Quant. Grav. 23, S179 (2006)] and Mitra et al. [Phys. Rev. D 77, 042002 (2008)]. Unlike past studies, here the MLR statistic enables us to compare quantitatively the performances of a variety of baselines searching for a SGWB signal in (simulated) data. Although we use simulated noise and SGWB signals for making these comparisons, our method can be straightforwardly applied on real data.Comment: 17 pages and 19 figure

Acoustic impedance estimation using a gradient-based algorithm with total variation semi-norm regularization

We present an algorithm to estimate blocky images of the subsurface acoustic impedance (AI) from seismic reflection data. We use the total variation semi-norm (TV) to regularize the inversion and promote blocky solutions which are, by virtue of the capability of TV to handle edges properly, adequate to model layered earth models with sharp contrasts. In addition, the use of the TV leads to a convex objective function that can be minimized using a gradientbased algorithm that only requires matrix-vector multiplications and no direct matrix inversion. The latter makes the algorithm numerically stable, easy to apply, and economic in terms of computational cost. Besides, given appropriate a priori information, the algorithm allows to easily incorporate into the inversion scheme the low frequency trend that is missing from the data. Numerical tests on noisy 2D synthetic and field data show that the proposed method is capable of providing consistent and blocky AI images that preserve edges and the subsurface layered structure.Facultad de Ciencias Astronómicas y Geofísica

Acoustic impedance estimation using a gradient-based algorithm with total variation semi-norm regularization

We present an algorithm to estimate blocky images of the subsurface acoustic impedance (AI) from seismic reflection data. We use the total variation semi-norm (TV) to regularize the inversion and promote blocky solutions which are, by virtue of the capability of TV to handle edges properly, adequate to model layered earth models with sharp contrasts. In addition, the use of the TV leads to a convex objective function that can be minimized using a gradientbased algorithm that only requires matrix-vector multiplications and no direct matrix inversion. The latter makes the algorithm numerically stable, easy to apply, and economic in terms of computational cost. Besides, given appropriate a priori information, the algorithm allows to easily incorporate into the inversion scheme the low frequency trend that is missing from the data. Numerical tests on noisy 2D synthetic and field data show that the proposed method is capable of providing consistent and blocky AI images that preserve edges and the subsurface layered structure.Facultad de Ciencias Astronómicas y Geofísica