Thong T. Do

Sparsity adaptive matching pursuit algorithm for practical compressed sensing

This paper presents a novel iterative greedy reconstruction algorithm for practical compressed sensing (CS), called the sparsity adaptive matching pursuit (SAMP). Compared with other state-of-the-art greedy algorithms, the most innovative feature of the SAMP is its capability of signal reconstruction without prior information of the sparsity. This makes it a promising candidate for many practical applications when the number of non-zero (significant) coefficients of a signal is not available. The proposed algorithm adopts a similar flavor of the EM algorithm, which alternatively estimates the sparsity and the true support set of the target signals. In fact, SAMP provides a generalized greedy reconstruction framework in which the orthogonal matching pursuit and the subspace pursuit can be viewed as its special cases. Such a connection also gives us an intuitive justification of trade-offs between computational complexity and reconstruction performance. While the SAMP offers a comparably theoretical guarantees as the best optimization-based approach, simulation results show that it outperforms many existing iterative algorithms, especially for compressible signals.

Fast and Efficient Compressive Sensing Using Structurally Random Matrices

This paper introduces a new framework to construct fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we prerandomize the sensing signal by scrambling its sample locations or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the resulting transform coefficients to obtain the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable to that of completely random sensing matrices. Numerical simulation results verify the validity of the theory and illustrate the promising potentials of the proposed sensing framework.

Fast compressive sampling with structurally random matrices

This paper presents a novel framework of fast and efficient compressive sampling based on the new concept of structurally random matrices. The proposed framework provides four important features, (i) It is universal with a variety of sparse signals, (ii) The number of measurements required for exact reconstruction is nearly optimal, (iii) It has very low complexity and fast computation based on block processing and linear filtering, (iv) It is developed on the provable mathematical model from which we are able to quantify trade-offs among streaming capability, computation/memory requirement and quality of reconstruction. All currently existing methods only have at most three out of these four highly desired features. Simulation results with several interesting structurally random matrices under various practical settings are also presented to verify the validity of the theory as well as to illustrate the promising potential of the proposed framework.

Distributed compressed video sensing

This paper proposes a novel framework called Distributed Compressed Video Sensing (DISCOS) - a solution for Distributed Video Coding (DVC) based on the recently emerging Compressed Sensing theory. The DISCOS framework compressively samples each video frame independently at the encoder. However, it recovers video frames jointly at the decoder by exploiting an interframe sparsity model and by performing sparse recovery with side information. In particular, along with global frame-based measurements, the DISCOS encoder also acquires local block-based measurements for block prediction at the decoder. Our interframe sparsity model mimics state-of-the-art video codecs: the sparsest representation of a block is a linear combination of a few temporal neighboring blocks that are in previously reconstructed frames or in nearby key frames. This model enables a block to be optimally predicted from its local measurements by l1-minimization. The DISCOS decoder also employs a sparse recovery with side information to jointly reconstruct a frame from its global measurements and its local block-based prediction. Simulation results show that the proposed framework outperforms the baseline compressed sensing-based scheme of intraframe-coding and intraframe-decoding by 8 – 10dB. Finally, unlike conventional DVC schemes, our DISCOS framework can perform most encoding operations in the analog domain with very low-complexity, making it be a promising candidate for real-time, practical applications where the analog to digital conversion is expensive, e.g., in Terahertz imaging.

Distributed Compressed Video Sensing

This paper proposes a novel framework called Distributed Compressed Video Sensing (DISCOS) - a solution for Distributed Video Coding (DVC) based on the recently emerging Compressed Sensing theory. The DISCOS framework compressively samples each video frame independently at the encoder. However, it recovers video frames jointly at the decoder by exploiting an interframe sparsity model and by performing sparse recovery with side information. In particular, along with global frame-based measurements, the DISCOS encoder also acquires local block-based measurements for block prediction at the decoder. Our interframe sparsity model mimics state-of-the-art video codecs: the sparsest representation of a block is a linear combination of a few temporal neighboring blocks that are in previously reconstructed frames or in nearby key frames. This model enables a block to be optimally predicted from its local measurements by l1-minimization. The DISCOS decoder also employs a sparse recovery with side information to jointly reconstruct a frame from its global measurements and its local block-based prediction. Simulation results show that the proposed framework outperforms the baseline compressed sensing-based scheme of intraframe-coding and intraframe-decoding by 8 – 10dB. Finally, unlike conventional DVC schemes, our DISCOS framework can perform most encoding operations in the analog domain with very low-complexity, making it be a promising candidate for real-time, practical applications where the analog to digital conversion is expensive, e.g., in Terahertz imaging.

Robust face recognition using locally adaptive sparse representation

This paper presents a block-based face-recognition algorithm based on a sparse linear-regression subspace model via locally adaptive dictionary constructed from past observable data (training samples). The local features of the algorithm provide an immediate benefit — the increase in robustness level to various registration errors. Our proposed approach is inspired by the way human beings often compare faces when presented with a tough decision: we analyze a series of local discriminative features (do the eyes match? how about the nose? what about the chin?…) and then make the final classification decision based on the fusion of local recognition results. In other words, our algorithm attempts to represent a block in an incoming test image as a linear combination of only a few atoms in a dictionary consisting of neighboring blocks in the same region across all training samples. The results of a series of these sparse local representations are used directly for recognition via either maximum likelihood fusion or a simple democratic majority voting scheme. Simulation results on standard face databases demonstrate the effectiveness of the proposed algorithm in the presence of multiple mis-registration errors such as translation, rotation, and scaling.

Sparse models and sparse recovery for ultra-wideband SAR applications

This paper presents a simple yet very effective time-domain sparse representation and associated sparse recovery techniques that can robustly process raw data-intensive ultra-wideband (UWB) synthetic aperture radar (SAR) records in challenging noisy and bandwidth management environments. Unlike most previous approaches in compressed sensing for radar in general and SAR in particular, we take advantage of the sparsity of the scene and the correlation between the transmitted and received signal directly in the raw time domain even before attempting image formation. Our framework can be viewed as a collection of practical sparsity-driven preprocessing algorithms for radar applications that restores and denoises raw radar signals at each aperture position independently, leading to a significant reduction in the memory requirement as well as the computational complexity of the sparse recovery process. Recovery results from real-world data collected by the U.S. Army Research Laboratory (ARL) UWB SAR systems illustrate the robustness and effectiveness of our proposed framework on two critical applications: 1) recovery of missing spectral information in multiple frequency bands and 2) adaptive extraction and/or suppression of radio frequency interference (RFI) signals from SAR data records.

Fast and efficient dimensionality reduction using Structurally Random Matrices

Structurally Random Matrices (SRM) are first proposed in [1] as fast and highly efficient measurement operators for large scale compressed sensing applications. Motivated by the bridge between compressed sensing and the Johnson-Lindenstrauss lemma [2] , this paper introduces a related application of SRMs regarding to realizing a fast and highly efficient embedding. In particular, it shows that a SRM is also a promising dimensionality reduction transform that preserves all pairwise distances of high dimensional vectors within an arbitrarily small factor ∈, provided that the projection dimension is on the order of O(∈−2 log3 N), where N denotes the number of d-dimensional vectors. In other words, SRM can be viewed as the sub-optimal Johnson-Lindenstrauss embedding that, however, owns very low computational complexity O(d log d) and highly efficient implementation that uses only O(d) random bits, making it a promising candidate for practical, large scale applications where efficiency and speed of computation are highly critical.

Recovery of missing spectral information in ultra-wideband synthetic aperture radar (SAR) data

In this paper, we present a novel technique to recover the missing spectral information in multiple frequency bands of ultra-wideband (UWB) synthetic aperture radar (SAR) data that are either corrupted (due to the presence of interference sources) or nonexistent (because of no transmission in the prohibited frequency bands). Although the spectral information is lost due to the contaminated and missing frequency bands, each backscatter receive data record can be modeled as a linear combination of the spectrally filtered and time-shifted versions of the transmitted waveform. Thus, the target information (range, amplitude, and phase) can be computed based on direct sparse recovery via orthogonal matching pursuit using a dictionary that contains many spectrally filtered and time-shifted versions of the transmitted waveform. On the other hand, the desired receive signal (with full spectral information) can be modeled as a linear combination of the time-shifted versions of the desired transmitted waveform (with full spectrum). Thus, once the target information is computed by the sparse recovery process using the receive data and the dictionary, the desired received signal can be reconstructed using the target information and the desired transmitted waveform. Using both simulation data and SAR data from the U.S. Army Research Laboratory (ARL) UWB SAR, we show that the proposed technique can successfully recover the information from the missing or corrupted frequency bands. The paper also compares the result to that using the conventional technique that simply zeros out the fast Fourier transform (FFT) bins that correspond to the corrupted frequency bands.

Robust video transmission using Layered Compressed Sensing

We propose a novel Layered Compressed Sensing (CS) approach for robust transmission of video signals over packet loss channels. In our proposed method, the encoder consists of a base layer and an enhancement layer. The base layer is a conventionally encoded bitstream and transmitted without any error protection. The additional enhancement layer is a stream of compressed measurements taken across slices of video signals for error-resilience. The decoder regards the corrupted base layer as the side information (SI) and employs a sparse recovery with SI to recover approximation of lost packets. By exploiting the SI at the decoder, the enhancement layer is required to transmit a minimal amount of compressed measurements for error protection that is only proportional to the amount of lost packets. Simulation results show that both compression efficiency and error-resilience capacity of the proposed scheme are competitive with those of other state-of-the-art robust transmission methods, in which Wyner-Ziv (WZ) coders often generate an enhancement layer. Thanks to the soft-decoding feature of sparse recovery algorithms, our CS-based scheme can avoid the cliff effect that often occurs with otherWyner-Ziv based schemes when the error rate is over the error correction capacity of the channel code. In addition, our result suggests that compressed sensing is actually closer to source coding with decoder side information than to conventional source coding.