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Compressed imaging by sparse random convolution

Aurélien Bourquard, Theo Lasser, Antonio Lopez

The theory of compressed sensing (CS) shows that signals can be acquired at sub-Nyquist rates if they are sufficiently sparse or compressible. Since many images bear this property, several acquisition models have been proposed for optical CS. An interesting approach is random convolution (RC). In contrast with single-pixel CS approaches, RC allows for the parallel capture of visual information on a sensor array as in conventional imaging approaches. Unfortunately, the RC strategy is difficult to implement as is in practical settings due to important contrast-to-noise-ratio (CNR) limitations. In this paper, we introduce a modified RC model circumventing such difficulties by considering measurement matrices involving sparse non-negative entries. We then implement this model based on a slightly modified microscopy setup using incoherent light. Our experiments demonstrate the suitability of this approach for dealing with distinct CS scenarii, including 1-bit CS

Optical Society of America2016

Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

Aurélien Bourquard, Hagay Kirshner, Michaël Unser, John Paul Ward

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and stochastic auto-regressive models, and exploit it for optimally choosing Sobolev parameters from available pixel values. To this aim, we use exact continuous-to-discrete mapping of the auto-regressive model that is based on symmetric exponential splines. The mapping is computationally efficient, and we exploit it for maximizing an approximated Gaussian likelihood function. We account for non-Gaussian Levy-type processes by deriving a more robust estimator that is based on the sample auto-correlation sequence. Both estimators use multiple initialization values for overcoming the local minima structure of the fitting criteria. Experimental image resizing results indicate that the auto-correlation criterion can cope better with non-Gaussian processes and model mismatch. Our work demonstrates the importance of the auto-correlation function in adaptive image interpolation and image modeling tasks, and we believe it is instrumental in other image processing tasks as well.

Ieee-Inst Electrical Electronics Engineers Inc2014

A Practical Inverse-Problem Approach to Digital Holographic Reconstruction

Emrah Bostan, Aurélien Bourquard, Christian Depeursinge, Nicolas Pavillon, Michaël Unser

In this paper, we propose a new technique for high-quality reconstruction from single digital holographic acquisitions. The unknown complex object field is found as the solution of a nonlinear inverse problem that consists in the minimization of an energy functional. The latter includes total-variation (TV) regularization terms that constrain the spatial amplitude and phase distributions of the reconstructed data. The algorithm that we derive tolerates downsampling, which allows to acquire substantially fewer measurements for reconstruction compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real off-axis holograms.

OSA2013