Sparse-coding denoising applied to reversible conformational switching of a porphyrin self-assembled monolayer induced by scanning tunnelling microscopy.

Scanning tunnelling microscopy (STM) was used to induce conformational molecular switching on a self-assembled monolayer of zinc-octaethylporphyrin on a graphite/tetradecane interface at room temperature. A reversible conformational change controlled by applying a tip voltage was observed. Consecutive STM images acquired at alternating tip voltages showed that at 0.4 V the porphyrin monolayer presents a molecular arrangement formed by alternate rows with two different types of structural conformations and when the potential is increased to 0.7 V the monolayer presents only one type of conformation. In this paper, we characterize these porphyrin conformational dynamics by analyzing the STM images, which were improved for better quality and interpretation by means of a denoising algorithm, adapted to process STM images from state of the art image processing and analysis methods. STM remains the best technique to 'see' and to manipulate the matter at atomic scale. A very sharp tip a few angstroms of the surface can provide images of molecules and atoms with a powerful resolution. However, these images are strongly affected by noise which is necessary to correct and eliminate. This paper is about new computational tools specifically developed to denoise the images acquired with STM. The new algorithms were tested in STM images, obtained at room temperature, of porphyrin monolayer which presents reversible conformational change in function of the tip bias voltage. Images with high resolution, acquired in real time, show that the porphyrins have different molecular arrangements whether the tip voltage is 0.4 V or 0.7 V.

Wavefront reconstruction in phase-shifting interferometry via sparse coding of amplitude and absolute phase.

Phase-shifting interferometry is a coherent optical method that combines high accuracy with high measurement speeds. This technique is therefore desirable in many applications such as the efficient industrial quality inspection process. However, despite its advantageous properties, the inference of the object amplitude and the phase, herein termed wavefront reconstruction, is not a trivial task owing to the Poissonian noise associated with the measurement process and to the 2π phase periodicity of the observation mechanism. In this paper, we formulate the wavefront reconstruction as an inverse problem, where the amplitude and the absolute phase are assumed to admit sparse linear representations in suitable sparsifying transforms (dictionaries). Sparse modeling is a form of regularization of inverse problems which, in the case of the absolute phase, is not available to the conventional wavefront reconstruction techniques, as only interferometric phase modulo-2π is considered therein. The developed sparse modeling of the absolute phase solves two different problems: accuracy of the interferometric (wrapped) phase reconstruction and simultaneous phase unwrapping. Based on this rationale, we introduce the sparse phase and amplitude reconstruction (SPAR) algorithm. SPAR takes into full consideration the Poissonian (photon counting) measurements and uses the data-adaptive block-matching 3D (BM3D) frames as a sparse representation for the amplitude and for the absolute phase. SPAR effectiveness is documented by comparing its performance with that of competitors in a series of experiments.

An alternating direction algorithm for total variation reconstruction of distributed parameters.

Augmented Lagrangian variational formulations and alternating optimization have been adopted to solve distributed parameter estimation problems. The alternating direction method of multipliers (ADMM) is one of such formulations/optimization methods. Very recently, the number of applications of the ADMM, or variants of it, to solve inverse problems in image and signal processing has increased at an exponential rate. The reason for this interest is that ADMM decomposes a difficult optimization problem into a sequence of much simpler problems. In this paper, we use the ADMM to reconstruct piecewise-smooth distributed parameters of elliptical partial differential equations from noisy and linear (blurred) observations of the underlying field. The distributed parameters are estimated by solving an inverse problem with total variation (TV) regularization. The proposed instance of the ADMM solves, in each iteration, an l(2) and a decoupled l(2) - l(1) optimization problems. An operator splitting is used to simplify the treatment of the TV regularizer, avoiding its smooth approximation and yielding a simple yet effective ADMM reconstruction method compared with previously proposed approaches. The competitiveness of the proposed method, with respect to the state-of-the-art, is illustrated in simulated 1-D and 2-D elliptical equation problems, which are representative of many real applications.