136 research outputs found
Phase Retrieval From Binary Measurements
We consider the problem of signal reconstruction from quadratic measurements
that are encoded as +1 or -1 depending on whether they exceed a predetermined
positive threshold or not. Binary measurements are fast to acquire and
inexpensive in terms of hardware. We formulate the problem of signal
reconstruction using a consistency criterion, wherein one seeks to find a
signal that is in agreement with the measurements. To enforce consistency, we
construct a convex cost using a one-sided quadratic penalty and minimize it
using an iterative accelerated projected gradient-descent (APGD) technique. The
PGD scheme reduces the cost function in each iteration, whereas incorporating
momentum into PGD, notwithstanding the lack of such a descent property,
exhibits faster convergence than PGD empirically. We refer to the resulting
algorithm as binary phase retrieval (BPR). Considering additive white noise
contamination prior to quantization, we also derive the Cramer-Rao Bound (CRB)
for the binary encoding model. Experimental results demonstrate that the BPR
algorithm yields a signal-to- reconstruction error ratio (SRER) of
approximately 25 dB in the absence of noise. In the presence of noise prior to
quantization, the SRER is within 2 to 3 dB of the CRB
Directional Bilateral Filters
We propose a bilateral filter with a locally controlled domain kernel for
directional edge-preserving smoothing. Traditional bilateral filters use a
range kernel, which is responsible for edge preservation, and a fixed domain
kernel that performs smoothing. Our intuition is that orientation and
anisotropy of image structures should be incorporated into the domain kernel
while smoothing. For this purpose, we employ an oriented Gaussian domain kernel
locally controlled by a structure tensor. The oriented domain kernel combined
with a range kernel forms the directional bilateral filter. The two kernels
assist each other in effectively suppressing the influence of the outliers
while smoothing. To find the optimal parameters of the directional bilateral
filter, we propose the use of Stein's unbiased risk estimate (SURE). We test
the capabilities of the kernels separately as well as together, first on
synthetic images, and then on real endoscopic images. The directional bilateral
filter has better denoising performance than the Gaussian bilateral filter at
various noise levels in terms of peak signal-to-noise ratio (PSNR)
Data Interpolants -- That's What Discriminators in Higher-order Gradient-regularized GANs Are
We consider the problem of optimizing the discriminator in generative
adversarial networks (GANs) subject to higher-order gradient regularization. We
show analytically, via the least-squares (LSGAN) and Wasserstein (WGAN) GAN
variants, that the discriminator optimization problem is one of interpolation
in -dimensions. The optimal discriminator, derived using variational
Calculus, turns out to be the solution to a partial differential equation
involving the iterated Laplacian or the polyharmonic operator. The solution is
implementable in closed-form via polyharmonic radial basis function (RBF)
interpolation. In view of the polyharmonic connection, we refer to the
corresponding GANs as Poly-LSGAN and Poly-WGAN. Through experimental validation
on multivariate Gaussians, we show that implementing the optimal RBF
discriminator in closed-form, with penalty orders , results in superior performance, compared to training GAN with
arbitrarily chosen discriminator architectures. We employ the Poly-WGAN
discriminator to model the latent space distribution of the data with
encoder-decoder-based GAN flavors such as Wasserstein autoencoders
Neuromorphic Sampling of Signals in Shift-Invariant Spaces
Neuromorphic sampling is a paradigm shift in analog-to-digital conversion
where the acquisition strategy is opportunistic and measurements are recorded
only when there is a significant change in the signal. Neuromorphic sampling
has given rise to a new class of event-based sensors called dynamic vision
sensors or neuromorphic cameras. The neuromorphic sampling mechanism utilizes
low power and provides high-dynamic range sensing with low latency and high
temporal resolution. The measurements are sparse and have low redundancy making
it convenient for downstream tasks. In this paper, we present a
sampling-theoretic perspective to neuromorphic sensing of continuous-time
signals. We establish a close connection between neuromorphic sampling and
time-based sampling - where signals are encoded temporally. We analyse
neuromorphic sampling of signals in shift-invariant spaces, in particular,
bandlimited signals and polynomial splines. We present an iterative technique
for perfect reconstruction subject to the events satisfying a density
criterion. We also provide necessary and sufficient conditions for perfect
reconstruction. Owing to practical limitations in meeting the sufficient
conditions for perfect reconstruction, we extend the analysis to approximate
reconstruction from sparse events. In the latter setting, we pose signal
reconstruction as a continuous-domain linear inverse problem whose solution can
be obtained by solving an equivalent finite-dimensional convex optimization
program using a variable-splitting approach. We demonstrate the performance of
the proposed algorithm and validate our claims via experiments on synthetic
signals
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