X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector, and the phase of the diffraction patterns is estimated using phase retrieval techniques. Most phase retrieval algorithms make the solution well-posed by relying on the constraints imposed by the overlapping region between neighboring diffraction pattern samples. As the overlap between neighboring diffraction patterns reduces, the problem becomes ill-posed, and the object cannot be recovered. To avoid the ill-posedness, we investigate the effect of regularizing the phase retrieval algorithm with image priors for various overlap ratios between the neighboring diffraction patterns. We show that the object can be faithfully reconstructed at low overlap ratios by regularizing the phase retrieval algorithm with image priors such as Total-Variation prior and Structure Tensor Prior. We also show the effectiveness of our proposed algorithm on real data acquired from an IC chip with a coherent X-ray beam.

Recently, time-of-flight (ToF) sensors have emerged as a promising three-dimensional sensing technology that can be manufactured inexpensively in a compact size. However, current state-of-the-art ToF sensors suffer from low spatial resolution due to physical limitations in the fabrication process. In this paper, we analyze the ToF sensor's output as a complex value coupling the depth and intensity information in a phasor representation. Based on this analysis, we introduce a novel multi-frame superresolution technique that can improve both spatial resolution in intensity and depth images simultaneously. We believe our proposed method can benefit numerous applications where high resolution depth sensing is desirable, such as precision automated navigation and collision avoidance.

Multi-focus microscope (MFM) provides a way to obtain 3D information by simultaneously capturing multiple focal planes. The naive method for MFM reconstruction is to stack the sub-images with alignment. However, the resolution in the z-axis in this method is limited by the number of acquired focal planes. In this work we build on a recent reconstruction algorithm for MFM, using information from multiple frames to improve the reconstruction quality. We propose two multiple-frame MFM image reconstruction algorithms: batch and recursive approaches. In the batch approach, we take multiple MFM frames and jointly estimate the 3D image and the motion for each frame. In the recursive approach, we utilize the reconstructed image from the previous frame. Experimental results show that the proposed algorithms produce a sequence of 3D object reconstruction with high quality that enable reconstruction of dynamic extended objects.

In this paper we address the Phase Retrieval problem, which aims to recover the phase of the Fourier transform of a signal when only magnitude measurements are available. Following recent developments in Phase Retrieval, the problem can be transformed into a convex semidefinite programming optimization problem, which can be solved using Matrix Completion techniques. In this paper the acquisition process is modeled using a likelihood function, which splits the original problem into two convex optimization problems, and alternates between the solution of each of them. To relate both convex problems we introduce a heuristic, which results in fast convergence of the proposed method.

We present a Bayesian approach for 3D image reconstruction of an extended object imaged with multi-focus microscopy (MFM). MFM simultaneously captures multiple sub-images of different focal planes to provide 3D information of the sample. The naive method to reconstruct the object is to stack the sub-images along the z-axis, but the result suffers from poor resolution in the z-axis. The maximum a posteriori framework provides a way to reconstruct a 3D image according to its observation model and prior knowledge. It jointly estimates the 3D image and the model parameters. Experimental results with synthetic and real experimental data show that it enables the high-quality 3D reconstruction of an extended object from MFM.

In this work we address the multispectral image classification problem from a Bayesian perspective. We develop an algorithm which utilizes the logistic regression function as the observation model in a probabilistic framework, Super-Gaussian (SG) priors which promote sparsity on the adaptive coefficients, and Variational inference to obtain estimates of all the model unknowns. The proposed algorithm is validated on both synthetic and real experiments and compared with other state-of-the-art methods, such as Support Vector Machine and Gaussian Processes, demonstrating its improved performance.

Sequence labeling aims at assigning a label to every sample of a signal (or pixel of an image) while considering the sequentiality (or vicinity) of the samples. To perform this task, many works in the literature first filter and then label the data. Unfortunately, the filtering, which is performed independently from the labeling, is far from optimal and frequently makes the latter task harder. In this paper, a novel approach that trains a Gaussian process classifier and estimates the coefficients of an optimal filter jointly is presented. The new approach, based on Bayesian modeling and alternating direction method of multipliers (ADMMs) optimization, performs both tasks simultaneously. All unknowns are treated as stochastic variables, which are estimated using variational inference and filtering and labeling are linked with the use of ADMM. In the experimental section, synthetic and real experiments are presented to compare the proposed method with other existing approaches.

Many real classification tasks are oriented to sequence (neighbor) labeling, that is, assigning a label to every sample of a signal while taking into account the sequentiality (or neighborhood) of the samples. This is normally approached by first filtering the data and then performing classification. In consequence, both processes are optimized separately, with no guarantee of global optimality. In this work we utilize Bayesian modeling and inference to jointly learn a classifier and estimate an optimal filterbank. Variational Bayesian inference is used to approximate the posterior distributions of all unknowns, resulting in an iterative procedure to estimate the classifier parameters and the filterbank coefficients. In the experimental section we show, using synthetic and real data, that the proposed method compares favorably with other classification/filtering approaches, without the need of parameter tuning.

In recent years, kernel methods, in particular support vector machines (SVMs), have been successfully introduced to remote sensing image classification. Their properties make them appropriate for dealing with a high number of image features and a low number of available labeled spectra. The introduction of alternative approaches based on (parametric) Bayesian inference has been quite scarce in the more recent years. Assuming a particular prior data distribution may lead to poor results in remote sensing problems because of the specificities and complexity of the data. In this context, the emerging field of nonparametric Bayesian methods constitutes a proper theoretical framework to tackle the remote sensing image classification problem. This paper exploits the Bayesian modeling and inference paradigm to tackle the problem of kernel-based remote sensing image classification. This Bayesian methodology is appropriate for both finite- and infinite-dimensional feature spaces. The particular problem of active learning is addressed by proposing an incremental/active learning approach based on three different approaches: 1) the maximum differential of entropies; 2) the minimum distance to decision boundary; and 3) the minimum normalized distance. Parameters are estimated by using the evidence Bayesian approach, the kernel trick, and the marginal distribution of the observations instead of the posterior distribution of the adaptive parameters. This approach allows us to deal with infinite-dimensional feature spaces. The proposed approach is tested on the challenging problem of urban monitoring from multispectral and synthetic aperture radar data and in multiclass land cover classification of hyperspectral images, in both purely supervised and active learning settings. Similar results are obtained when compared to SVMs in the supervised mode, with the advantage of providing posterior estimates for classification and automatic parameter learning. Comparison with random sampling as well as standard active learning methods such as margin sampling and entropy-query-by-bagging reveals a systematic overall accuracy gain and faster convergence with the number of queries.

We propose a novel design for light field image acquisition based on compressive sensing principles. By placing a randomly coded mask at the aperture of a camera, incoherent measurements of the light passing through different parts of the lens are encoded in the captured images. Each captured image is a random linear combination of different angular views of a scene. The encoded images are then used to recover the original light field image via a novel Bayesian reconstruction algorithm. Using the principles of compressive sensing, we show that light field images with a large number of angular views can be recovered from only a few acquisitions. Moreover, the proposed acquisition and recovery method provides light field images with high spatial resolution and signal-to-noise-ratio, and therefore is not affected by limitations common to existing light field camera designs. We present a prototype camera design based on the proposed framework by modifying a regular digital camera. Finally, we demonstrate the effectiveness of the proposed system using experimental results with both synthetic and real images.

Every day, a huge amount of video data is generated for different purposes and applications. Fast and accurate algorithms for efficient video search and retrieval are therefore essential. The interesting properties of sparse representation and the new sampling theory named Compressive Sensing (CS) constitute the core of the new approach to video representation and retrieval we are presenting in this paper. Once the representation (where sparsity is expected) has been chosen and the observations have been taken, the proposed approach utilizes Bayesian modeling and inference to tackle the retrieval problem. In order to speed up the inference process the use of Principal Components Analysis (PCA) to provide an alternative representation of the frames is analyzed. Experimental results validate the proposed approach whose robustness against noise is also examined.