Following up on yesterday's entry today we have other reconstruction solvers for both phase retrieval and
ptychography. The following demos are directly downloadable from the Local Approximations in Signal and Image Processing (LASIP) website. There you can find:

- Sparse Phase Amplitude Reconstruction (SPAR)
- 4f SPAR phase retrieval
- Decoupled augmented Lagrangian (D-AL)
- Compressive sensing computational ghost imaging (CSGI)
- Compressive ptychographical coherent diffractive imaging

Attendant documents explaining what each of these routines does is given below (except for the ptychography paper that does not seem out yet).

Computational ghost imaging: advanced compressive sensing (CS) technique by Vladimir Katkovnik, Jaakko Astola (a preprint is here) The abstract reads:

A novel efficient variational technique for speckle imaging is discussed. It is developed with the main motivation to filter noise, to wipe out the typical diffraction artifacts and to achieve crisp imaging. A sparse modeling is used for the wave field at the object plane in order to overcome the loss of information due to the ill-posedness of forward propagation image formation operators. This flexible and data adaptive modeling relies on the recent progress in sparse imaging and compressive sensing (CS). Being in line with the general formalism of CS, we develop an original approach to wave field reconstruction.^{7}In this paper we demonstrate this technique in its application for computational amplitude ghost imaging (GI), where a spatial light modulator (SLM) is used in order to generate a speckle wave field sensing a transmitted mask object.

High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude by Vladimir Katkovnik and Jaakko Astola ( a preprint is here). The abstract reads:

We apply a nonlocal adaptive spectral transform for sparse modeling of phase and amplitude of a coherent wave field. The reconstruction of this wave field from complex-valued Gaussian noisy observations is considered. The problem is formulated as a multiobjective constrained optimization. The developed iterative algorithm decouples the inversion of the forward propagation operator and the filtering of phase and amplitude of the wave field. It is demonstrated by simulations that the performance of the algorithm, both visually and numerically, is the current state of the art.

Phase retrieval via spatial light modulator phase modulation in 4f optical setup: numerical inverse imaging with sparse regularization for phase and amplitude by Vladimir Katkovnik and Jaakko Astola. The abstract reads:

The 4f optical setup is considered with a wave field modulation by a spatial light modulator located in the focal plane of the first lens. Phase as well as amplitude of the wave field are reconstructed from noisy multiple-intensity observations. The reconstruction is optimal due to a constrained maximum likelihood formulation of the problem. The proposed algorithm is iterative with decoupling of the inverse of the forward propagation of the wave field and the filtering of phase and amplitude. The sparse modeling of phase and amplitude enables the advanced high-accuracy filtering and sharp imaging of the complex-valued wave field. Artifacts typical for the conventional algorithms (wiggles, ringing, waves, etc.) and attributed to optical diffraction can be suppressed by the proposed algorithm.

Advanced phase retrieval: maximum likelihood technique with sparse regularization of phase and amplitude by Artem Migukin, Vladimir Katkovnik, Jaakko Astola. The abstract reads:

Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase. The algorithm is derived in terms of a constrained maximum likelihood, where the wave field reconstruction is performed using a number of noisy intensity-only observations with a zero-mean additive Gaussian noise. The developed algorithm enables the optimal solution for the object wave field reconstruction. Our goal is an improvement of the reconstruction quality with respect to the conventional algorithms. Sparse regularization results in advanced reconstruction accuracy, and numerical simulations demonstrate significant enhancement of imaging.

Advanced multi-plane phase retrieval using Graphic Processing Unit: augmented Lagrangian technique with sparse regularization by
Artem Migukin, Vladimir Katkovnik, Jaakko Astola The abstract reads:

In our work we demonstrate a computational method of phase retrieval realized for various propagation models. The effects, arising due to the wave field propagation in an optical setup, lead to significant distortions in measurements; therefore the reconstructed wave fields are noisy and corrupted by different artifacts (e.g. blurring, "waves" on boards, etc.). These disturbances are hard to be specified, but could be suppressed by filtering. The contribution of this paper concerns application of an adaptive sparse approximation of the object phase and amplitude in order to improve imaging. This work is considered as a further development and improvement of the variational phase-retrieval algorithm originated in 1. It is shown that the sparse regularization enables a better reconstruction quality and substantial enhancement of imaging. Moreover, it is demonstrated that an essential acceleration of the algorithm can be obtained by a commodity graphic processing unit, what is crucial for processing of large images.

Phase retrieval with background compensation in 4f configuration: advanced augmented Lagrangian technique for amplitude object by Artem Migukin, Mostafa Agour, Vladimir Katkovnik. The abstract reads:

Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred and corrupted by various artifacts such as irregular waves, spots, etc. These disturbances, arising due to many factors such as non-idealities of optical system (misalignment, focusing errors), dust on optical elements, reflections, vibration, are hard to be localized and specified. It is assumed that there is a generalized pupil function at the object plane which describes aberrations in the coherent imaging system manifested at the sensor plane. Here we propose a novel two steps phase-retrieval algorithm to compensate these distortions. We first estimate the cumulative disturbance, called background, using special calibration experiments. Then, we use this background for reconstruction of the object amplitude and phase. The second part of the algorithm is based on the maximum likelihood approach and, in this way, targeted on the optimal amplitude and phase reconstruction from noisy data. Numerical experiments demonstrate that the developed algorithm enables the compensation of various typical distortions of the optical track so sharp object imaging for a binary test-chart can be achieved.

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