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.

We present a primal-dual interior point method (IPM) with a novel preconditioner to solve the ℓ1-norm regularized least square problem for nonnegative sparse signal reconstruction. IPM is a second-order method that uses both gradient and Hessian information to compute effective search directions and achieve super-linear convergence rates. It therefore requires many fewer iterations than first-order methods such as iterative shrinkage/thresholding algorithms (ISTA) that only achieve sub-linear convergence rates. However, each iteration of IPM is more expensive than in ISTA because it needs to evaluate an inverse of a Hessian matrix to compute the Newton direction. We propose to approximate each Hessian matrix by a diagonal matrix plus a rank-one matrix. This approximation matrix is easily invertible using the Sherman-Morrison formula, and is used as a novel preconditioner in a preconditioned conjugate gradient method to compute a truncated Newton direction. We demonstrate the efficiency of our algorithm in compressive 3D volumetric image reconstruction. Numerical experiments show favorable results of our method in comparison with previous interior point based and iterative shrinkage/thresholding based algorithms.

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.

Incoherent holography has recently attracted significant research interest due to its flexibility for a wide variety of light sources. In this paper, we use compressive sensing to reconstruct a three-dimensional volumetric object from its two-dimensional Fresnel incoherent correlation hologram. We show how compressed sensing enables reconstruction without out-of-focus artifacts, when compared to conventional back-propagation recovery. Finally, we analyze the reconstruction guarantees of the proposed approach both numerically and theoretically and compare that with coherent holography.

Despite decades of study, robust shadow detection remains difficult, especially within a single color image. We describe a new approach to detect shadow boundaries in images of outdoor scenes lit only by the sun and sky. The method first extracts visual features of candidate edges that are motivated by physical models of illumination and occluders. We feed these features into a Support Vector Machine (SVM) that was trained to discriminate between most-likely shadow-edge candidates and less-likely ones. Finally, we connect edges to help reject non-shadow edge candidates, and to encourage closed, connected shadow boundaries. On benchmark shadow-edge data sets from Lalonde et al. and Zhu et al., our method showed substantial improvements when compared to other recent shadow-detection methods based on statistical learning.

We present a technique to construct increased-resolution images from multiple photos taken without moving the camera or the sensor. Like other super-resolution techniques, we capture and merge multiple images, but instead of moving the camera sensor by sub-pixel distances for each image, we change masks in the lens aperture and slightly defocus the lens. The resulting capture system is simpler, and tolerates modest mask registration errors well. We present a theoretical analysis of the camera and image merging method, show both simulated results and actual results from a crudely modified consumer camera, and compare its results to robust ‘blind’ methods that rely on uncontrolled camera displacements.