5,366 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
Artifact reduction for separable non-local means
It was recently demonstrated [J. Electron. Imaging, 25(2), 2016] that one can
perform fast non-local means (NLM) denoising of one-dimensional signals using a
method called lifting. The cost of lifting is independent of the patch length,
which dramatically reduces the run-time for large patches. Unfortunately, it is
difficult to directly extend lifting for non-local means denoising of images.
To bypass this, the authors proposed a separable approximation in which the
image rows and columns are filtered using lifting. The overall algorithm is
significantly faster than NLM, and the results are comparable in terms of PSNR.
However, the separable processing often produces vertical and horizontal
stripes in the image. This problem was previously addressed by using a
bilateral filter-based post-smoothing, which was effective in removing some of
the stripes. In this letter, we demonstrate that stripes can be mitigated in
the first place simply by involving the neighboring rows (or columns) in the
filtering. In other words, we use a two-dimensional search (similar to NLM),
while still using one-dimensional patches (as in the previous proposal). The
novelty is in the observation that one can use lifting for performing
two-dimensional searches. The proposed approach produces artifact-free images,
whose quality and PSNR are comparable to NLM, while being significantly faster.Comment: To appear in Journal of Electronic Imagin
Fast Separable Non-Local Means
We propose a simple and fast algorithm called PatchLift for computing
distances between patches (contiguous block of samples) extracted from a given
one-dimensional signal. PatchLift is based on the observation that the patch
distances can be efficiently computed from a matrix that is derived from the
one-dimensional signal using lifting; importantly, the number of operations
required to compute the patch distances using this approach does not scale with
the patch length. We next demonstrate how PatchLift can be used for patch-based
denoising of images corrupted with Gaussian noise. In particular, we propose a
separable formulation of the classical Non-Local Means (NLM) algorithm that can
be implemented using PatchLift. We demonstrate that the PatchLift-based
implementation of separable NLM is few orders faster than standard NLM, and is
competitive with existing fast implementations of NLM. Moreover, its denoising
performance is shown to be consistently superior to that of NLM and some of its
variants, both in terms of PSNR/SSIM and visual quality
Fast Cross-Polytope Locality-Sensitive Hashing
We provide a variant of cross-polytope locality sensitive hashing with
respect to angular distance which is provably optimal in asymptotic sensitivity
and enjoys hash computation time. Building on a recent
result (by Andoni, Indyk, Laarhoven, Razenshteyn, Schmidt, 2015), we show that
optimal asymptotic sensitivity for cross-polytope LSH is retained even when the
dense Gaussian matrix is replaced by a fast Johnson-Lindenstrauss transform
followed by discrete pseudo-rotation, reducing the hash computation time from
to . Moreover, our scheme achieves
the optimal rate of convergence for sensitivity. By incorporating a
low-randomness Johnson-Lindenstrauss transform, our scheme can be modified to
require only random bitsComment: 14 pages, 6 figure
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