We demonstrate that the phase of randomized complex-valued projections of real-valued signals preserves information about the angle, i.e., the correlation, between those signals. This information can be exploited to design quantized angle-preserving embeddings, which represent such correlations using a nite bit-rate. The proposed embeddings generalize known results on binary embeddings and 1-bit compressive sensing and allow us to explore the trade-o between number of measurements and number of bits per measurement, given the bit rate. The freedom provided by this trade-off, which has also been observed in quantized Johnson-Lindenstrauss embeddings, can improve performance at reduced rate in a number of applications.
We propose a rate-efficient, feature-agnostic approach for encoding image features for cloud-based nearest neighbor search.
We extract quantized random projections of the image features under consideration, transmit these to the cloud server, and
perform matching in the space of the quantized projections. The advantage of this approach is that, once the underlying feature
extraction algorithm is chosen for maximum discriminability and retrieval performance (e.g., SIFT, or eigen-features),
the random projections guarantee a rate-efficient representation and fast server-based matching with negligible loss in accuracy.
Using the Johnson-Lindenstrauss Lemma, we show that pair-wise distances between the underlying feature vectors
are preserved in the corresponding quantized embeddings. We report experimental results of image retrieval on two image
databases with different feature spaces; one using SIFT features and one using face features extracted using a variant of
the Viola-Jones face recognition algorithm. For both feature spaces, quantized embeddings enable accurate image retrieval
combined with improved bit-rate efficiency and speed of matching, when compared with the underlying feature spaces.
Recent work has demonstrated the power of sparse models and representations in signal processing applications
and has provided the community with computational tools to use it. In this paper we explore the use of sparsity
in localization and beamforming when capturing multiple broadband sources using a sensor array. Specifically,
we reformulate the wideband signal acquisition as a joint/group sparsity problem in a combined frequency-space
domain. Under this formulation the signal is sparse in the spatial domain but has common support in all
frequencies. Using techniques from the model-based compressive sensing literature we demonstrate that it is
possible to robustly capture, localize and often reconstruct multiple signals present in the scene.
We present a low-complexity method for compression of raw Synthetic Aperture Radar (SAR) data. Raw SAR
data is typically acquired using a satellite or airborne platform without sufficient computational capabilities
to process the data and generate a SAR image on-board. Hence, the raw data needs to be compressed and
transmitted to the ground station, where SAR image formation can be carried out. To perform low-complexity
compression, our method uses 1-dimensional transforms, followed by quantization and entropy coding. In contrast
to previous approaches, which send uncompressed or Huffman-coded bits, we achieve more efficient entropy
coding using an arithmetic coder that responds to a continuously updated probability distribution. We present
experimental results on compression of raw Ku-SAR data. In those we evaluate the effect of the length of
the transform on compression performance and demonstrate the advantages of the proposed framework over a
state-of-the-art low complexity scheme called Block Adaptive Quantization (BAQ).
Compressed Sensing (CS) is a new signal acquisition technique that allows sampling of sparse signals using
significantly fewer measurements than previously thought possible. On the other hand, a fusion frame is a new
signal representation method that uses collections of subspaces instead of vectors to represent signals. This work
combines these exciting new fields to introduce a new sparsity model for fusion frames. Signals that are sparse
under the new model can be compressively sampled and uniquely reconstructed in ways similar to sparse signals
using standard CS. The combination provides a promising new set of mathematical tools and signal models useful
in a variety of applications.
With the new model, a sparse signal has energy in very few of the subspaces of the fusion frame, although it
needs not be sparse within each of the subspaces it occupies. We define a mixed ℓ1/ℓ2 norm for fusion frames.
A signal sparse in the subspaces of the fusion frame can thus be sampled using very few random projections
and exactly reconstructed using a convex optimization that minimizes this mixed ℓ1/ℓ2 norm. The sampling
conditions we derive are very similar to the coherence and RIP conditions used in standard CS theory.
Compressive sensing is a new data acquisition technique that aims to measure sparse and compressible signals at close to their intrinsic information rate rather than their Nyquist rate. Recent results in compressive sensing show that a sparse or compressible signal can be reconstructed from very few measurements with an incoherent, and
even randomly generated, dictionary. To date the hardware implementation of compressive sensing analog-to-digital systems has not been straightforward. This paper explores the use of Sigma-Delta quantizer architecture to implement such a system. After examining the challenges of using Sigma-Delta with a randomly generated
compressive sensing dictionary, we present efficient algorithms to compute the coefficients of the feedback loop. The experimental results demonstrate that Sigma-Delta relaxes the required analog filter order and quantizer precision. We further demonstrate that restrictions on the feedback coefficient values and stability constraints impose a small penalty on the performance of the
Sigma-Delta loop, while they make hardware implementations significantly simpler.
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