Efficient and Stable Acoustic Tomography Using Sparse Reconstruction Methods

We study an acoustic tomography problem and propose a new inversion technique based on sparsity. Acoustic tomography observes the parameters of the medium that influence the speed of sound propagation. In the human body, the parameters that mostly influence the sound speed are temperature and density, in the ocean - temperature and current, in the atmosphere - temperature and wind. In this study, we focus on estimating temperature in the atmosphere using the information on the average sound speed along the propagation path. The latter is practically obtained from travel time measurements. We propose a reconstruction algorithm that exploits the concept of sparsity. Namely, the temperature is assumed to be a linear combination of some functions (e.g. bases or set of different bases) where many of the coefficients are known to be zero. The goal is to find the non-zero coefficients. To this end, we apply an algorithm based on linear programming that under some constrains finds the solution with minimum l0 norm. This is actually equivalent to the fact that many of the unknown coefficients are zeros. Finally, we perform numerical simulations to assess the effectiveness of our approach. The simulation results confirm the applicability of the method and demonstrate high reconstruction quality and robustness to noise

Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics

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 Cram\'er-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

Groebner Basis Methods for Multichannel Sampling with Unknown Offsets

In multichannel sampling, several sets of sub-Nyquist sampled signal values are acquired. The offsets between the sets are unknown, and have to be resolved, just like the parameters of the signal itself. This problem is nonlinear in the offsets, but linear in the signal parameters. We show that when the basis functions for the signal space are related to polynomials, we can express the joint offset and signal parameter estimation as a set of polynomial equations. This is the case for example with polynomial signals or Fourier series. The unknown offsets and signal parameters can be computed exactly from such a set of polynomials using Gröbner bases and Buchberger’s algorithm. This solution method is developed in detail after a short and tutorial overview of Gröbner basis methods. We then address the case of noisy samples, and consider the computational complexity, exploring simplifications due to the special structure of the problem

Dynamic Measurement of Room Impulse Responses using a Moving Microphone

A novel technique for the recording of large sets of room impulse responses or head-related transfer functions is presented. The technique uses a microphone or a loudspeaker moving with constant speed. Given a setup (e.g. length of the room impulse response), a careful choice of the recording parameters (excitation signal, speed of movement) is shown to lead to the reconstruction of all impulse responses along the trajectory. In the case of moving element along a circle, the maximal angular speed is given in function of the length of the impulse response, its maximal temporal frequency, the speed of sound propagation and the radius of the circle. As result of this theory, it is shown that head-related transfer functions sampled at $44.1~$kHz can be measured at all angular positions along the horizontal plane in less than one second. The presented theory is compared with a real system implementation using a precision moving microphone holder. The practical setup is discussed together with its limitations

Acoustic tomography for estimating temperature and wind flow

We consider the problem of reconstructing superimposed temperature and wind flow fields from acoustic measurements. A new technique based solely on acoustic wave propagation is presented. In contrast to the usual straight ray assumption, a bent ray model is considered in order to achieve higher accuracy. We also develop a lab size experiment for temperature estimation

Three-Dimensional Motion Estimation of Objects for Video Coding

Three-dimensional (3-D) motion estimation is applied to the problem of motion compensation for video coding. We suppose that the video sequence consists of the perspective projections of a collection of rigid bodies which undergo a rototranslational motion. Motion compensation can be performed on the sequence once the shape of the objects and the motion parameters are determined. We show that the motion equations of a rigid body can be formulated as a nonlinear dynamic system whose state is represented by the motion parameters and by the scaled depths of the object feature points. An extended Kalman filter is used to estimate both the motion and the object shape parameters simultaneously. The inclusion of the shape parameters in the estimation procedure adds a set of constraints to the filter equations that appear to be essential for reliable motion estimation. Our experiments show that the proposed approach gives two advantages. First, the filter can give more reliable estimates in the presence of measurement noise in comparison with other motion estimators that separately compute motion and structure. Second, the filter can efficiently track abrupt motion changes. Moreover, the structure imposed by the model implies that the reconstructed motion is very natural as opposed to more common block-based schemes. Also, the parameterization of the model allows for a very efficient coding of the motion informatio

Adapting the Sample Size in Texture Synthesis

Starting from a sample of a given size, texture synthesis algorithms are used to create larger texture images. A good algorithm produces synthesized textures that are pixelwise different but perceptually indistinguishable from the original image. The sample image should be chosen ensuring that it contains a number of pattern repetitions sufficient to produce valuable synthesis results. Since textures can be characterized by patterns of different dimensions, this must be done in an adaptive way. In this article, we propose a method that automatically adapts the sample size for natural textures synthesis, according to the different patterns dimensions. The method is based on the measure of the spatial dependence between the texture pixel values. This measure is used to estimate the size of the smallest texture window that is still perceived as texture by human observers. The sample size is determined from this measure by applying a multiplicative factor that depends on the algorithm used for synthesis. We perform a simple subjective experiment to estimate this factor for three different synthesis algorithms. We show that the measure of spatial dependence based on the correlation between pixels performs well when it is used to adapt the sample size

Signal Reconstruction from Multiple Unregistered Sets of Samples using Groebner Bases

We present a new method for signal reconstruction from multiple sets of samples with unknown offsets. We rewrite the reconstruction problem as a set of polynomial equations in the unknown signal parameters and the offsets between the sets of samples. Then, we construct a Groebner basis for the corresponding affine variety. The signal parameters can then easily be derived from this Groebner basis. This provides us with an elegant solution method for the initial nonlinear problem. We show two examples for the reconstruction of polynomial signals and Fourier series

Room impulse responses measurement using a moving microphone

In this paper, we present a technique to record a large set of room impulse responses using a microphone moving along a tra jectory. The technique processes the signal recorded by the microphone to reconstruct the signals that would have been recorded at all possible spatial positions along the array. The speed of movement of the microphone is shown to be the key factor for the reconstruction. This fast method of recording spatial impulse responses can also be applied for the recording of head-related transfer functions