Balancing Sparsity and Rank Constraints in Quadratic Basis Pursuit

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for analyzing the trade off between the sparsity and low rank constraints in these approaches which not only helps to provide guidelines to adjust the weights between the aforementioned constraints, but also enables new simulation strategies for evaluating performance. We then provide simulation results for phase retrieval and phase calibration cases both to demonstrate the consistency of the proposed method with other approaches and to evaluate the change of performance with different weights for the sparsity and low rank structure constraints

Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially (i) gains with different amplitude and the same phase, (ii) gains with the same amplitude and different phase and (iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided

CBC4CS (Convex Blind Calibration for Compressive Sensing) Toolbox

CBC4CS is a Matlab package to reproduce the convex blind calibration experiments of the following papers:[1] Cagdas Bilen, Gilles Puy, Rémi Gribonval, Laurent Daudet, "Convex Optimization Approaches for Blind Sensor Calibration using Sparsity", IEEE Transationc on Signal Processing 2014 .[2] ,Cagdas Bilen, Gilles Puy, Rémi Gribonval, Laurent Daudet, "Blind Phase Calibration in Sparse Recovery", EUSIPCO 2013

A multi-view video codec based on H.264

H.264 is the current state-of-the-art monoscopic video codec providing almost twice the coding efficiency with the same quality comparing the previous codecs. With the increasing interest in 3D TV, multi-view video sequences that are provided by multiple cameras capturing the three dimensional objects and/or scene are more widely used. Compressing multi-view sequences independently with H.264 (simulcast) is not efficient since the redundancy between the closer cameras is not exploited. In order to reduce these redundancies, we propose a Multi-View Video Codec based on H.264 using disparity estimation/compensation as well as motion estimation/compensation. In order to effectively search for disparity/motion without increasing computational complexity, we modified the buffering structure of H.264 and implemented several referencing modes. Our results show that for closely located cameras, our codec outperforms simulcast H.264 coding. For sparsely located cameras, our method can still improve coding gain depending on the video characteristics

Solving Time Domain Audio Inverse Problems using Nonnegative Tensor Factorization

International audienceNonnegative matrix and tensor factorization (NMF and NTF) are important tools for modeling nonnegative data, which gained increasing popularity in various fields, a significant one of which is audio processing. However there are still many problems in audio processing, for which the NMF (or NTF) model has not been successfully utilized. In this work we propose a new algorithm based on NMF (and NTF) in the short-time Fourier domain for solving a large class of audio inverse problems with missing or corrupted time domain samples. The proposed approach overcomes the difficulty of employing a model in the frequency domain to recover time domain samples with the help of probabilistic modeling. Its performance is demonstrated for the applications such as audio declipping and declicking (never solved with NMF/NTF modeling prior to this work), joint audio declipping/declicking and source separation (never solved with NMF/NTF modeling or any other method prior to this work), compressive sampling recovery and informed source separation (a low complexity encoding scheme that is possible with the proposed approach and has never been proposed prior to this work)

Blind Calibration for Phase Shifts in Compressive Systems

International audienceWe consider a blind calibration problem in a compressed sensing measurement system in which each sensor introduces an unknown phase shift to be determined. We show that this problem can be approached similarly to the problem of phase retrieval from quadratic measurements. Furthermore, when dealing with measurements generated from multiple unknown (but sparse) signals, we extend the approach for phase retrieval to solve the calibration problem in order to recover the signals jointly along with the phase shift parameters. The proposed methods are shown to have significantly better recovery performance than individual recovery of the input signals when the number of input signals are sufficiently large

Blind Phase Calibration in Sparse Recovery

International audienceWe consider a {\em blind} calibration problem in a compressed sensing measurement system in which each sensor introduces an unknown phase shift to be determined. We show that this problem can be approached similarly to the problem of phase retrieval from quadratic measurements. Furthermore, when dealing with measurements generated from multiple unknown (but sparse) signals, we extend the approach for phase retrieval to solve the calibration problem in order to recover the signals jointly along with the phase shift parameters. Additionally, we propose an alternative optimization method with less computation complexity and memory requirements. The proposed methods are shown to have significantly better recovery performance than individual recovery of the input signals when the number of input signals are sufficiently large

SUBJECTIVE EVALUATION OF EFFECTS OF SPECTRAL AND SPATIAL REDUNDANCY REDUCTION ON STEREO IMAGES

Human visual system is more sensitive to luminance than to chrominance. In order to reduce information that is not perceived by human visual system, color channels are downsampled while keeping luminance as original. Similarly in stereo case, human visual system uses high frequency information from the high resolution image of the mixed resolution image pair. By downsampling one of the pair, higher compression is achieved in stereo image coding. In this paper, we have examined downsampling color channels in higher ratios in color stereo image pairs. In our experiments, we have used “double-stimulus continuous-quality scale ” (DSCQS) method. We have found out that the depth perception is not changed by compression or filtering. However, in order to keep perceived image quality similar to the original stereo pair, filtering should be applied to chrominance but not to luminance channels. 1