Publications by Year: 2012

C. Hu and Y. M. Lu, “Adaptive time-sequential binary sensing for high dynamic range imaging,” in Proc. SPIE Conference on Advanced Photon Counting Techniques VI, Baltimore, MD, 2012.Abstract

We present a novel image sensor for high dynamic range imaging. The sensor performs an adaptive one-bit quantization at each pixel, with the pixel output switched from 0 to 1 only if the number of photons reaching that pixel is greater than or equal to a quantization threshold. With an oracle knowledge of the incident light intensity, one can pick an optimal threshold (for that light intensity) and the corresponding Fisher information contained in the output sequence follows closely that of an ideal unquantized sensor over a wide range of intensity values. This observation suggests the potential gains one may achieve by adaptively updating the quantization thresholds. As the main contribution of this work, we propose a time-sequential threshold-updating rule that asymptotically approaches the performance of the oracle scheme. With every threshold mapped to a number of ordered states, the dynamics of the proposed scheme can be modeled as a parametric Markov chain. We show that the frequencies of different thresholds converge to a steady-state distribution that is concentrated around
the optimal choice. Moreover, numerical experiments show that the theoretical performance measures (Fisher information and Cramer-Rao bounds) can be achieved by a maximum likelihood estimator, which is guaranteed to find globally optimal solution due to the concavity of the log-likelihood functions. Compared with conventional image sensors and the strategy that utilizes a constant single-photon threshold considered in previous work, the
proposed scheme attains orders of magnitude improvement in terms of sensor dynamic ranges.

C. Hu, L. Cheng, and Y. M. Lu, “Graph-Based regularization for color image demosaicking,” in Proc. IEEE International Conference on Image Processing, Orlando, FL, 2012.Abstract

We present a novel regularization framework for demosaicking by viewing images as smooth signals defined on weighted graphs. The restoration problem is formulated as a minimization of variation of these graph-domain signals. As an initial step, we build a weight matrix which measures the similarity between every pair of pixels, from an estimate of the full color image. Subsequently, a two-stage optimization is carried out: first, we assume that the graph Laplacian is signal dependent and solve a non-quadratic problem by gradient descent; then, we pose a variational problem on graphs with a fixed Laplacian, subject to the constraint of consistency given by available samples in each color channel. Performance evaluation shows that our approach can improve existing demosaicking methods both quantitively and visually, by reducing color artifacts.

Z. Sadeghipoor, Y. M. Lu, and S. Süsstrunk, “Optimal spectral sensitivity functions for single sensor color imaging,” in Proc. SPIE Conference on Digital Photography VIII, Burlingame, 2012.Abstract

A cost-effective and convenient approach for color imaging is to use a single sensor and mount a color filter array
(CFA) in front of it, such that at each spatial position the scene information in one color channel is captured. To
estimate the missing colors at each pixel, a demosaicing algorithm is applied to the CFA samples. Besides the
filter arrangement and the demosaicing method, the spectral sensitivity functions of the CFA filters considerably
affect the quality of the demosaiced image. In this paper, we extend the algorithm presented by Lu and Vetterli,
originally proposed for designing the optimum CFA, to compute the optimum spectral sensitivities. The proposed
algorithm solves a constrained optimization problem to find optimum spectral sensitivities and the corresponding
linear demosaicing method. An important constraint for this problem is the smoothness of spectral sensitivities,
which is imposed by modeling these functions as a linear combination of several smooth kernels. Simulation
results verify the effectiveness of the proposed algorithm in finding optimal spectral sensitivity functions, which
outperform measured camera sensitivity functions.

A. Agaskar and Y. M. Lu, “Uncertainty principles for signals defined on graphs: Bounds and characterizations,” in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, Kyoto, 2012.Abstract

The classical uncertainty principle provides a fundamental tradeoff in the localization of a signal in the time and frequency domains. In this paper we describe a similar tradeoff for signals defined on graphs. We describe the notions of "spread" in the graph and spectral domains, using the eigenvectors of the graph Laplacian as a surrogate Fourier basis. We then describe how to find signals that, among all signals with the same spectral spread, have the smallest graph spread about a given vertex. For every possible spectral spread, the desired signal is the solution to an eigenvalue problem. Since localization in graph and spectral domains is a desirable property of the elements of wavelet frames on graphs, we compare the performance of some existing wavelet transforms to the obtained bound.

See, also, the extended journal version: A. Agaskar and Y. M. Lu, A Spectral Graph Uncertainty Principle, IEEE Transactions on Information Theory, to appear.
Y. Xiong and Y. M. Lu, “Blind estimation and low-rate sampling of sparse MIMO systems with common support,” in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, Kyoto, 2012.Abstract

We present a blind estimation algorithm for multi-input and multi-output (MIMO) systems with sparse common support. Key to the proposed algorithm is a matrix generalization of the classical annihilating filter technique, which allows us to estimate the nonlinear parameters of the channels through an efficient and noniterative procedure. An attractive property of the proposed algorithm is that it only needs the sensor measurements at a narrow frequency band. By exploiting this feature, we can derive efficient sub-Nyquist sampling schemes which significantly reduce the number of samples that need to be retained at each sensor. Numerical simulations verify the accuracy of the proposed estimation algorithm and its robustness in the presence of noise.

M. N. Do and Y. M. Lu, “Multidimensional Filter Banks and Multiscale Geometric Representations,” Foundation and Trends in Signal Processing, vol. 5, no. 3, pp. 157-264, 2012.Abstract

Thanks to the explosive growth of sensing devices and capabilities, multidimensional (MD) signals — such as images, videos, multispectral images, light fields, and biomedical data volumes — have become ubiquitous.
Multidimensional filter banks and the associated constructions provide a unified framework and an efficient computational tool in the formation, representation, and processing of these multidimensional data sets. In this survey we aim to provide a systematic development of the theory and constructions of multidimensional filter banks. We thoroughly review several tools that have been shown to be particularly effective in the design and analysis of multidimensional filter banks, including sampling lattices, multidimensional bases and frames, polyphase representations, Gröbner bases, mapping methods, frequency domain constructions, ladder structures and lifting schemes. We then focus on the construction of filter banks and signal representations that can capture directional and geometric features, which are unique and key properties of many multidimensional signals. Next, we study the connection between iterated multidimensional filter banks in the discrete domain and the associated multiscale signal representations in the continuous domain through a directional multiresolution analysis framework. Finally, we show several examples to demonstrate the power of multidimensional filter banks and geometric signal representations in applications.

F. Yang, Y. M. Lu, L. Sbaiz, and M. Vetterli, “Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics,” IEEE Transactions on Image Processing, vol. 21, no. 4, pp. 1421-1436, 2012. Extended Version with Complete ProofAbstract

We study a new image sensor that is reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. To analyze its performance, we formulate the oversampled binary sensing scheme as a parameter estimation problem based on quantized Poisson statistics. We show that, with a single-photon quantization threshold and large oversampling factors, the Cramér-Rao lower bound (CRLB) of the estimation variance approaches that of an ideal unquantized sensor, that is, as if there were no quantization in the sensor measurements. Furthermore, the CRLB is shown to be asymptotically achievable by the maximum likelihood estimator (MLE). By showing that the log-likelihood function of our problem is concave, we guarantee the global optimality of iterative algorithms in finding the MLE. Numerical results on both synthetic data and images taken by a prototype sensor verify our theoretical analysis and demonstrate the effectiveness of our image reconstruction algorithm. They also suggest the potential application of the oversampled binary sensing scheme in high dynamic range photography.