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## Friday, March 27, 2015

### Deep Transform: Time-Domain Audio Error Correction via Probabilistic Re-Synthesis, Cocktail Party Source Separation via Probabilistic Re-Synthesis

From the same author, two preprints using deep neural networks to perform a task that is traditionally in other domain such as communication/information theory (Error Correction) or advanced matrix factorization (BSS). Welcome to the great convergence:

In the process of recording, storage and transmission of time-domain audio signals, errors may be introduced that are difficult to correct in an unsupervised way. Here, we train a convolutional deep neural network to re-synthesize input time-domain speech signals at its output layer. We then use this abstract transformation, which we call a deep transform (DT), to perform probabilistic re-synthesis on further speech (of the same speaker) which has been degraded. Using the convolutive DT, we demonstrate the recovery of speech audio that has been subject to extreme degradation. This approach may be useful for correction of errors in communications devices.

Deep Transform: Cocktail Party Source Separation via Probabilistic Re-Synthesis by Andrew J.R. Simpson
In cocktail party listening scenarios, the human brain is able to separate competing speech signals. However, the signal processing implemented by the brain to perform cocktail party listening is not well understood. Here, we trained two separate convolutive autoencoder deep neural networks (DNN) to separate monaural and binaural mixtures of two concurrent speech streams. We then used these DNNs as convolutive deep transform (CDT) devices to perform probabilistic re-synthesis. The CDTs operated directly in the time-domain. Our simulations demonstrate that very simple neural networks are capable of exploiting monaural and binaural information available in a cocktail party listening scenario.

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## Thursday, March 26, 2015

### Thesis: Compressive Power Spectral Analysis by Dyonisius Ariananda

Compressive Power Spectral Analysis by Dyonisius Ariananda
At the heart of digital signal processing (DSP) are the sampling and quantization processes, which convert analog signals into discrete samples and which are implemented in the form of analog to digital converters (ADCs). In some recent applications, there is an increased demand for DSP applications to process signals having a very wide bandwidth. For such signals, the minimum allowable sampling rate is also very high and this has put a very high demand on the ADCs in terms of power consumption. Recently, the emergence of compressive sampling (CS) has offered a solution that allows us to reconstruct the original signal from samples collected from a sampling device operating at sub-Nyquist rate. The application of CS usually involves applying an additional constraint such as a sparsity constraint on the original signal. However, there are also applications where the signal to deal with has a high bandwidth (and thus sub-Nyquist rate sampling is still important) but where only the second-order statistics (instead of the original signal) are required to be reconstructed. In the latter case, depending on the characteristics of the signals, it might be possible to reconstruct the second-order statistics of the received analog signal from its sub-Nyquist rate samples without applying any additional constraints on the original signals. This idea is the key starting point of this thesis.

We first focus on time-domain wide-sense stationary (WSS) signals and introduce a method for reconstructing their power spectrum from their sub-Nyquist rate samples without requiring the signal or the power spectrum to be sparse. Our method is examined both in the time- and frequency-domain and the solution is computed using a simple least-squares (LS) approach, which produces a solution if the rank condition of the resulting system matrix is satisfied. To satisfy this rank condition, two options of sampling design are proposed, one of which is the so-called multi-coset sampling. It is show in this thesis that any of the so-called sparse ruler can produce a multi-coset sampling design that guarantees the full rank condition of the system matrix, and thus the optimal compression is achieved by a minimal sparse ruler.

While the approach in the previous paragraph is related to time-domain signals, we could extend the discussion about the power spectrum reconstruction from sub-Nyquist rate samples in the context of the spatial-domain signal, which is defined as a sequence of outputs of the antennas in the antenna array at a particular time instant. Given the compressed spatial domain signals, which are obtained from the output of a uniform linear array (ULA) with some antennas turned off, of particular interest is to reconstruct the angular power spectrum, from which the direction of arrival (DOA) of the sources can generally be located. In this thesis, a method to estimate the angular power spectrum and the DOA of possibly fully correlated sources based on second-order statistics of the compressed spatial-domain signals is proposed by employing a so-called dynamic array which is built upon the so-called underlying ULA. In this method, we present the spatial correlation matrices of the output of the dynamic active antenna arrays at all time slots as a linear function of the spatial correlation matrix of the entire underlying uniform array and we solve for this last correlation matrix using LS. The required theoretical condition to ensure the full column rank condition of the system matrix is formulated and designs are proposed to satisfy this condition.

Next, we consider both spatio-angular and time-frequency domains and propose a compressive periodogram reconstruction method as our next contribution. We introduce the multibin model, where the entire band is divided into equal-size bins such that the spectra at two frequencies or angles, whose distance is at least equal to the bin size, are uncorrelated. This model results in a circulant structure in the so-called coset correlation matrix, which enables us to introduce a strong compression. We propose the sampling patterns based on a circular sparse ruler to guarantee the full column rank condition of the system matrix and to allow the LS reconstruction of the periodogram. We also provide a method for the case when the bin size is reduced such that the spectra at two frequencies or angles, whose distance is larger than the bin size, can still be correlated.

To combine frequency and DOA processing, we also introduce a compressive two-dimensional (2D) frequency- and angular-domain power spectrum reconstruction for multiple uncorrelated time-domain WSS signals received from different sources by a linear array of antennas. We perform spatial-domain compression by deactivating some antennas in an underlying ULA and time-domain compression by multi-coset sampling.

Finally, we propose a compressive cyclic spectrum reconstruction approach for wide-sense cyclostationary (WSCS) signals, where we consider sub-Nyquist rate samples produced by non-uniform sampling. This method is proposed after first observing that the block Toeplitz structure emerges in theWSCS signal correlation matrix. This structure is exploited to solve the WSCS signal correlation matrix by LS. The condition for the system matrix to have full column rank is provided and some possible non-uniform sampling designs to satisfy this full column rank condition are presented.

Based on all the works that have been done, we have found that focusing on reconstructing the statistical measure of the received signals has significantly relax the sampling requirements and the constraints on both the statistics and the signals themselves. Hence, we would like to conclude that, for given tasks of applications in hand, we should ask ourselves whether statistical measure reconstruction is sufficient since the answer for this question will likely to determine how we should collect the data from the observed phenomena. This underlines the importance of awareness on what kind of information is necessary and sufficient for the tasks in hand before conducting the sensing/sampling process.

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### Real-time Dynamic MRI Reconstruction using Stacked Denoising Autoencoder

Great convergence, here we come ! From the paper:
The dataset contains about 17424 volumes; and multiple slices in each volume. In total we have used about 100,000 images for training the SDAE's...Unfortunately, for these datasets, the fully sampled k-space scans are not available. Therefore the reconstruction results obtained from [8] is taken as the basis images for comparison.

Using time dependent images reconstructed from some unknown algorithm and comparing it with the temporal reconstruction capability of Deep Neural Networks is a first step and it may set the comparison with a CS reconstruction in an unfair light. But the next step ought to be obvious :-) Thank you Angshul for this provocative preprint (provocative because deep neural nets have very little theory associated with them whereas there is more of it for compressive sensing and MRI)

Real-time Dynamic MRI Reconstruction using Stacked Denoising Autoencoder by Angshul Majumdar

In this work we address the problem of real-time dynamic MRI reconstruction. There are a handful of studies on this topic; these techniques are either based on compressed sensing or employ Kalman Filtering. These techniques cannot achieve the reconstruction speed necessary for real-time reconstruction. In this work, we propose a new approach to MRI reconstruction. We learn a non-linear mapping from the unstructured aliased images to the corresponding clean images using a stacked denoising autoencoder (SDAE). The training for SDAE is slow, but the reconstruction is very fast - only requiring a few matrix vector multiplications. In this work, we have shown that using SDAE one can reconstruct the MRI frame faster than the data acquisition rate, thereby achieving real-time reconstruction. The quality of reconstruction is of the same order as a previous compressed sensing based online reconstruction technique.

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## Wednesday, March 25, 2015

### Improving M-SBL for Joint Sparse Recovery using a Subspace Penalty

This is very interesting. In the area of sparsity seeking solvers M-SBL is with AMP one of the interesting solvers to follow. This is in part due to the good results Zhilin Zhang got with block sparsity and non sparse signals in the past.The authors of the following paper change the regularization term of that algorithm and seem to have even better phase transitions for sparse signals. Without further ado:

Improving M-SBL for Joint Sparse Recovery using a Subspace Penalty by Jong Chul Ye, Jong Min Kim, Yoram Bresler
The multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to reveal that the seemingly least related state-of-art MMV joint sparse recovery algorithms - M-SBL (multiple sparse Bayesian learning) and subspace-based hybrid greedy algorithms - have a very important link. More specifically, we show that replacing the $\log\det(\cdot)$ term in M-SBL by a rank proxy that exploits the spark reduction property discovered in subspace-based joint sparse recovery algorithms, provides significant improvements. In particular, if we use the Schatten-$p$ quasi-norm as the corresponding rank proxy, the global minimiser of the proposed algorithm becomes identical to the true solution as $p \rightarrow 0$. Furthermore, under the same regularity conditions, we show that the convergence to a local minimiser is guaranteed using an alternating minimization algorithm that has closed form expressions for each of the minimization steps, which are convex. Numerical simulations under a variety of scenarios in terms of SNR, and condition number of the signal amplitude matrix demonstrate that the proposed algorithm consistently outperforms M-SBL and other state-of-the art algorithms.

I wonder how that change of the regularization proxy would change Zhilin's codes

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## Tuesday, March 24, 2015

### LiSens, Photometric stereo using BRDF dictionaries, CS-MUVI

Aswin Sankaranarayanan just let me know of the following papers:

Hi Igor
Hope you are well.
I wanted to point out a few recent papers.

1) LiSens http://arxiv.org/abs/1503.04267

This paper describes a multi-pixel extension to the single pixel camera. We show that it is possible to obtain videos at spatial resolution of nearly mega-pixel resolution and at 10 frames-per-second using a sensor array with 1000s of pixel.

2) Photometric stereo using BRDF dictionaries. http://arxiv.org/abs/1503.04265

This paper is on shape estimation of non-Lambertian objects. While not mainstream CS work, at the heart of this work is a bilinear problem that we solve using some interesting techniques.

3) CS-MUVI (journal version) http://arxiv.org/abs/1503.02727

This paper uses motion-flow models for video CS using the single-pixel camera. We demonstrate many results on real data obtained from our lab prototype. This is the extended version of a conference publication in 2012.

Both LiSens and the photometric stereo work will appear in the proceedings of Intl. conf. computational photography (ICCP), 2015.

Am hoping this will be interesting to you and the broader nuit-blanche readership.
Outstanding ! thanks Aswin

LiSens --- A Scalable Architecture for Video Compressive Sensing by Jian Wang, Mohit Gupta, Aswin C. Sankaranarayanan
The measurement rate of cameras that take spatially multiplexed measurements by using spatial light modulators (SLM) is often limited by the switching speed of the SLMs. This is especially true for single-pixel cameras where the photodetector operates at a rate that is many orders-of-magnitude greater than the SLM. We study the factors that determine the measurement rate for such spatial multiplexing cameras (SMC) and show that increasing the number of pixels in the device improves the measurement rate, but there is an optimum number of pixels (typically, few thousands) beyond which the measurement rate does not increase. This motivates the design of LiSens, a novel imaging architecture, that replaces the photodetector in the single-pixel camera with a 1D linear array or a line-sensor. We illustrate the optical architecture underlying LiSens, build a prototype, and demonstrate results of a range of indoor and outdoor scenes. LiSens delivers on the promise of SMCs: imaging at a megapixel resolution, at video rate, using an inexpensive low-resolution sensor.

A Dictionary-based Approach for Estimating Shape and Spatially-Varying Reflectance  by Zhuo Hui, Aswin C. Sankaranarayanan
We present a technique for estimating the shape and reflectance of an object in terms of its surface normals and spatially-varying BRDF. We assume that multiple images of the object are obtained under fixed view-point and varying illumination, i.e, the setting of photometric stereo. Assuming that the BRDF at each pixel lies in the non-negative span of a known BRDF dictionary, we derive a per-pixel surface normal and BRDF estimation framework that requires neither iterative optimization techniques nor careful initialization, both of which are endemic to most state-of-the-art techniques. We showcase the performance of our technique on a wide range of simulated and real scenes where we outperform competing methods.

Video Compressive Sensing for Spatial Multiplexing Cameras using Motion-Flow Models by Aswin C. Sankaranarayanan, Lina Xu, Christoph Studer, Yun Li, Kevin Kelly, Richard G. Baraniuk

Spatial multiplexing cameras (SMCs) acquire a (typically static) scene through a series of coded projections using a spatial light modulator (e.g., a digital micro-mirror device) and a few optical sensors. This approach finds use in imaging applications where full-frame sensors are either too expensive (e.g., for short-wave infrared wavelengths) or unavailable. Existing SMC systems reconstruct static scenes using techniques from compressive sensing (CS). For videos, however, existing acquisition and recovery methods deliver poor quality. In this paper, we propose the CS multi-scale video (CS-MUVI) sensing and recovery framework for high-quality video acquisition and recovery using SMCs. Our framework features novel sensing matrices that enable the efficient computation of a low-resolution video preview, while enabling high-resolution video recovery using convex optimization. To further improve the quality of the reconstructed videos, we extract optical-flow estimates from the low-resolution previews and impose them as constraints in the recovery procedure. We demonstrate the efficacy of our CS-MUVI framework for a host of synthetic and real measured SMC video data, and we show that high-quality videos can be recovered at roughly 60× compression.

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## Monday, March 23, 2015

### Python version of SPGL1 - implementation -

David Relyea just let me know of his porting the famous SPGL1 solver to Python, woohoo !
Hi Igor,

I've entirely ported the Matlab version of SPGL1 to python. It has full functionality (it heavily leverages numpy) and I haven't caught any bugs in it at all, so I'm letting everyone know. I got the ok from Michael Friedlander to distribute it (under the same license, of course). It's at https://github.com/drrelyea/SPGL1_python_port. Please let people know!

I also intend to clean it up a bit and have it added to scikit-learn, as it's the fastest L1 solver I know of that can handle complex numbers.

All the best,

David Relyea
Thanks David !

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## Sunday, March 22, 2015

### Sunday Morning Insight: Muon Tomography of Fukushima Daiichi's reactor #1

Here is a followup to a previous Sunday Morning Insight (Muon Tomography as a Moore's Law Enabled Technology). I took notice of it on Rod Adams twitter feed: The result of a 26-day Muon Tomography study of Fukushima Daiichi reactor 1. The report is entitled: Reactor imaging technology for fuel debris detection by cosmic ray muon Measurement status report in Unit-1 and features a two angle tomography of reactor #1 and the attendant Spent Fuel Pool in that same building.

Several remarks:
• The detectors are not low enough to image the reactor material where it probably is (i.e. at the bottom of the Pressure Containment Vessel).
• There is a discrepancy between the readings of detector 1 and 2. It seems to my untrained eye that this may have to do with detector 1 having a line of sight that includes the spent fuel pool whereas detector 2 has less contribution from that component. The reconstruction algorithm using readings from detector 1 might be putting more emphasis from the higher density of material in the spent fuel than contribution from the reactor core.
• The algorithm performing the reconstruction does not seem to be using the scattering component as featured in Imaging Damaged Reactors and Volcanoes, Let us note that 26 days is the same ballpark as the 6 weeks mentioned in that study.

Relevant: Sunday Morning Insight: Muon Tomography as a Moore's Law Enabled Technology

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## Saturday, March 21, 2015

### Saturday Morning Video: The Automatic Statistician, Certifying and removing Disparate Impact, Machine Learning et Entreprise

Here is the video and attendant slides of the Paris Machine Learning Meetup #7 Season 2. I am providing the links that start directly at the beginning of each talk.
All the slides and videos of the previous Paris Machine Learning Meetups are available here.

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## Friday, March 20, 2015

### Around The Blogs in 78 Hours

We got pre-selected into the iLab competition, woohoo !

Ben Lorica just wrote about tensors in Let’s build open source tensor libraries for data science . One of the author whose work was featured in that blog, to one of my comment there:

...Indeed, there are many types of decompositions on tensors, we are certainly not the only ones to be working on them. The paper you point out about tensors states that there can be ill-posed tensors, which is true. In fact, there is another paper which states that most tensor problems are NP-hard http://arxiv.org/abs/0911.1393 However, the tensors we study, which are relevant for machine learning, turn out to be "easy cases" establish is that under some very reasonable non-degeneracy. I talk about some of these points in the podcast that Ben will post in due course. Stay tuned!

Within the blogs we generally cover, here are some items that grabbed my interest:

Sebastien
Djalil
John
Charles
Afonso
Dirk
Ben
While on Nuit Blanche, we had:

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### Infinite-dimensional $\ell^1$ minimization and function approximation from pointwise data

Infinite-dimensional $\ell^1$ minimization and function approximation from pointwise data by Ben Adcock
We consider the problem of approximating a function from finitely-many pointwise samples using $\ell^1$ minimization techniques. In the first part of this paper, we introduce an infinite-dimensional approach to this problem. Three advantages of this approach are as follows. First, it provides interpolatory approximations in the absence of noise. Second, it does not require a priori bounds on the expansion tail in order to be implemented. In particular, the truncation strategy we introduce as part of this framework is completely independent of the function being approximated. Third, it allows one to explain the crucial role weights play in the minimization, namely, that of regularizing the problem and removing so-called aliasing phenomena. In the second part of this paper we present a worst-case error analysis for this approach. We provide a general recipe for analyzing the performance of such techniques for arbitrary deterministic sets of points. Finally, we apply this recipe to show that weighted $\ell^1$ minimization with Jacobi polynomials leads to an optimal, convergent method for approximating smooth, one-dimensional functions from scattered data.

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