Prasad Sudhakar

Compressive Imaging and Characterization of Sparse Light Deflection Maps

Light rays incident on a transparent object of uniform refractive index undergo deflections, which uniquely characterize the surface geometry of the object. Associated with each point on the surface is a deflection map (or spectrum) which describes the pattern of deflections in various directions. This article presents a novel method to efficiently acquire and reconstruct sparse deflection spectra induced by smooth object surfaces. To this end, we leverage the framework of compressed sensing (CS) in a particular implementation of a schlieren deflectometer, i.e., an optical system providing linear measurements of deflection spectra with programmable spatial light modulation patterns. In particular, we design those modulation patterns on the principle of spread spectrum CS for reducing the number of observations. Interestingly, the ability of our device to simultaneously observe the deflection spectra on a dense discretization of the object surface is related to a particular multiple measurement vector mode...

Compressive schlieren deflectometry

Schlieren deflectometry aims at characterizing the deflections undergone by refracted incident light rays at any surface point of a transparent object. For smooth surfaces, each surface location is actually associated with a sparse deflection map (or spectrum). This paper presents a novel method to compressively acquire and reconstruct such spectra. This is achieved by altering the way deflection information is captured in a common Schlieren Deflectometer, i.e., the deflection spectra are indirectly observed by the principle of spread spectrum compressed sensing. These observations are realized optically using a 2-D Spatial Light Modulator (SLM) adjusted to the corresponding sensing basis and whose modulations encode the light deviation subsequently recorded by a CCD camera. The efficiency of this approach is demonstrated experimentally on the observation of few test objects. Further, using a simple parameterization of the deflection spectra we show that relevant key parameters can be directly computed using the measurements, avoiding full reconstruction.

A sparse smoothing approach for Gaussian Mixture Model based Acoustic-to-Articulatory Inversion

It is well-known that the performance of the Gaussian Mixture Model (GMM) based Acoustic-to-Articulatory Inversion (AAI) improves by either incorporating smoothness constraint directly in the inversion criterion or smoothing (low-pass filtering) estimated articulator trajectories in a post-processing step, where smoothing is performed independently of the inversion. As the low-pass filtering is independent of inversion, the smoothed articulator trajectory samples no longer remain optimal as per the inversion criterion. In this work, we propose a sparse smoothing technique which constrains the smoothed articulator trajectory to be different from the estimated trajectory only at a sparse subset of samples while simultaneously achieving the required degree of smoothness. Inversion experiments on the articulatory database show that the sparse smoothing achieves an AAI performance similar to that using low-pass filtering but in sparse smoothing ~15% (on average) of the samples in the smoothed articulator trajectory remain identical to those in the estimated articulator trajectory thereby preserve their AAI optimality as opposed to 0% in low-pass filtering.

Some uniqueness results in sparse convolutive source separation

The fundamental problems in the traditional frequency domain approaches to convolutive blind source separation are 1) arbitrary permutations and 2) arbitrary scaling in each frequency bin of the estimated filters or sources. These ambiguities are corrected by taking into account some specific properties of the filters or sources, or both. This paper focusses on the filter permutation problem, assuming the absence of the scaling ambiguity, investigating the use of temporal sparsity of the filters as a property to aid permutation correction. Theoretical and experimental results bring out the potential as well as the extent to which sparsity can be used as a hypothesis to formulate a well posed permutation problem.