Compressive correlation holography.

We propose and demonstrate a compressive sensing (CS) framework for correlation holography. This is accomplished by adopting the principle of compressive sensing and thresholding in the two-point intensity correlation. The measurement matrix and the sensing matrix that are required for applying the CS framework here are systematically extracted from the random illuminations of the laser speckle data. Reconstruction results using CS, CS with thresholding, and intensity correlation are compared. Our study reveals that liminal CS requires far fewer samples for the reconstruction of the hologram and has wide application in image reconstruction.

Adaptive multifocus image fusion using block compressed sensing with smoothed projected Landweber integration in the wavelet domain.

The need for image fusion in current image processing systems is increasing mainly due to the increased number and variety of image acquisition techniques. Image fusion is the process of combining substantial information from several sensors using mathematical techniques in order to create a single composite image that will be more comprehensive and thus more useful for a human operator or other computer vision tasks. This paper presents a new approach to multifocus image fusion based on sparse signal representation. Block-based compressive sensing integrated with a projection-driven compressive sensing (CS) recovery that encourages sparsity in the wavelet domain is used as a method to get the focused image from a set of out-of-focus images. Compression is achieved during the image acquisition process using a block compressive sensing method. An adaptive thresholding technique within the smoothed projected Landweber recovery process reconstructs high-resolution focused images from low-dimensional CS measurements of out-of-focus images. Discrete wavelet transform and dual-tree complex wavelet transform are used as the sparsifying basis for the proposed fusion. The main finding lies in the fact that sparsification enables a better selection of the fusion coefficients and hence better fusion. A Laplacian mixture model fit is done in the wavelet domain and estimation of the probability density function (pdf) parameters by expectation maximization leads us to the proper selection of the coefficients of the fused image. Using the proposed method compared with the fusion scheme without employing the projected Landweber (PL) scheme and the other existing CS-based fusion approaches, it is observed that with fewer samples itself, the proposed method outperforms other approaches.

Particle-filter-based phase estimation in digital holographic interferometry.

In this paper, we propose a particle-filter-based technique for the analysis of a reconstructed interference field. The particle filter and its variants are well proven as tracking filters in non-Gaussian and nonlinear situations. We propose to apply the particle filter for direct estimation of phase and its derivatives from digital holographic interferometric fringes via a signal-tracking approach on a Taylor series expanded state model and a polar-to-Cartesian-conversion-based measurement model. Computation of sample weights through non-Gaussian likelihood forms the major contribution of the proposed particle-filter-based approach compared to the existing unscented-Kalman-filter-based approach. It is observed that the proposed approach is highly robust to noise and outperforms the state-of-the-art especially at very low signal-to-noise ratios (i.e., especially in the range of -5 to 20 dB). The proposed approach, to the best of our knowledge, is the only method available for phase estimation from severely noisy fringe patterns even when the underlying phase pattern is rapidly varying and has a larger dynamic range. Simulation results and experimental data demonstrate the fact that the proposed approach is a better choice for direct phase estimation.

Recursive framework for joint inpainting and de-noising of photographic films.

We address the problem of inpainting noisy photographs. We present a recursive image recovery scheme based on the unscented Kalman filter (UKF) to simultaneously inpaint identified damaged portions in an image and suppress film-grain noise. Inpainting of the missing observations is guided by a mask-dependent reconstruction of the image edges. Prediction within the UKF is based on a discontinuity-adaptive Markov random field prior that attempts to preserve edges while achieving noise reduction in uniform regions. We demonstrate the capability of the proposed method with many examples.

A recursive filter for despeckling SAR images.

This correspondence proposes a recursive algorithm for noise reduction in synthetic aperture radar imagery. Excellent despeckling in conjunction with feature preservation is achieved by incorporating a discontinuity-adaptive Markov random field prior within the unscented Kalman filter framework through importance sampling. The performance of this method is demonstrated on both synthetic and real examples.