Wearables, Sensables, and Opportuniteis at CES 2015

ApplySci released a summary on wearable healthcare devices on CES 2015. And I quoted below. ApplySci commented that "Samsung's Simband is best positioned to take wearables into medical monitoring". Note that in Simband, PPG are used to monitor heart rate for fitness tracking and health monitoring, and I've already obtained the superior PPG-based heart rate estimation algorithms for it. Some general frameworks have been published/under review by IEEE Transaction on Biomedical Engineering. You can check my website for more details: https://sites.google.com/site/researchbyzhang/

It was the year of Digital Health and Wearable Tech at CES.  Endless watches tracked vital signs (and many athletes exercised tirelessly to prove the point).   New were several ear based fitness monitors (Brag), and some interesting TENS pain relief wearables (Quell).  Many companies provided  monitoring for senior citizens, and the most interesting only notified caregivers when there was a change in learned behavior (GreenPeak).  Senior companion robots were missing, although robots capable of household tasks were present (Oshbot).  3D printing was big (printed Pizza)–but where were 3d printed bones and organs?  Augmented reality was popular (APX,Augmenta)–but mostly for gaming or industrial use.  AR for health is next.

Two companies continue to stand out in Digital Health.  Samsung’s Simband  is best positioned to take wearables into  medical monitoring, with its multitude of sensors, open platform, and truly advanced health technologies. And  MC10‘s electronics that bend, stretch, and flex will disrupt home diagnosis, remote monitoring, and smart medical devices.

We see two immediate opportunities.  The brain, and the pulse.

1.  A few companies at CES claimed to monitor brain activity, and one savvy brand (Muse) provided earphones with soothing sounds while a headband monitored attention.  While these gadgets were fun to try, noone at CES presented extensive brain state interpretation to address cognitive and emotional issues.

2.  Every athlete at CES used a traditional finger based pulse sensor.  A slick wearable that can forgo the finger piece will make pulse oximetry during sports fun, instead of awkward.  As with every gadget, ensuring accuracy is key, as blind faith in wearables can be dangerous.

ApplySci looks forward to CES 2016, and the many breakthroughs to be discovered along the way, many of which will be featured at Wearable Tech + Digital Health NYC 2015.

A smart-watch for elders independent of Wi-Fi network

We have seen many smartwatches made by major IT giants and many startups. Now here is another smartwatch made by a crowdfunded startup, Lively.

The senior monitoring sensor system operates independently of a Wi-Fi network. It relies on the Lively Hub, with its own cellular network.

The watch gives medicine reminders, or alerts when medicine has been missed. It has an emergency button contacts a dispatcher and alerts family members. Fitness tracking features, such as steps taken, are included, and can be viewed by the wearer or family. The wearable is waterproof and can be worn in the shower.

ECG on the run: Continuous ECG surveillance of marathon athletes is feasible

Article From: http://www.sciencedaily.com/releases/2014/10/141029084122.htm?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+sciencedaily%2Fhealth_medicine+%28Health+%26+Medicine+News+--+ScienceDaily%29

The condition of an athlete's heart has for the first time been accurately monitored throughout the duration of a marathon race. The real-time monitoring was achieved by continuous electrocardiogram (ECG) surveillance and data transfer over the public mobile phone network to a telemedicine centre along the marathon route. This new development in cardiac testing in endurance athletes, said investigators, "would allow instantaneous diagnosis of potentially fatal rhythm disorders."

Following trails in two marathon races, the investigators now describe online ECG surveillance as feasible and "a promising preventive concept." They explain in their first report of the technique how "in the case of life-threatening arrhythmias, the emergency services located along the running track could be alerted to take the runners at risk out of the race and start extended cardiologic diagnostics and treatment."

The investigators, from the Center for Cardiovascular Telemedicine, Charité-Universitätsmedizin in Berlin, present their results at the first European Congress on e-Cardiology and e-Health, with a full report published in the European Journal of Preventive Cardiology.

Proof of the method's concept was achieved during two marathon races in Germany, in each of which five healthy runners (mean age 41.7 years) were equipped with a small ECG device and smart phone worn on the arm. Data transfer between the ECG monitor and phone was by Bluetooth technology. The ECG data were streamed from the device to the investigators' telemedicine centre in Berlin, where the data were monitored live and stored for later analysis.

During the trials all ten participants completed the two marathons without problems (in a mean time of 3h 37min) but there were differences in the quality of ECG streaming. In the first race, with more than 7000 runners and 150,000 spectators, there was virtually no accurate streaming from the ECG device because of errors in both the Bluetooth connection and connectivity of the phone to the mobile phone network.

New software to connect both devices was thus introduced for the second race six months later (with more than 15,000 runners and 300,000 spectators), and the athletes were asked to wear each device (ECG and smart phone) on the same arm. As a result of the changes, the quality of streaming ECG data was "excellent," with mean transfer time for an ECG wave complex measured at just 72 seconds.

Thus, on this second attempt feasibility was demonstrated in the two essential parameters: rapid transfer time of ECG data; and the continuity of ECG information between individual mobile phones and the medical centre.

Next on the agenda, say the investigators, is a miniaturised ECG device "to improve comfort and acceptance." And generally, they add, the system should ideally "be able to transmit ECG signals reliably, even under extreme conditions, such as running, with extensive body movements of the sweating athletes. Moreover, there should be no interruption in ECG data transfer within a mobile phone network, even under the condition of an extreme workload caused by thousands of mobile phone customers (athletes and spectators) allocated in a very limited geographical area."

As background to the study the investigators note that sudden cardiac death is rare -- though not unknown -- among marathon runners and other endurance athletes. In 2012 one 42-year-old runner died at the end of the London marathon, the event's second death in three years. All such tragic events are widely publicised -- as in the case of UK soccer player Fabrice Muamba, whose heart stopped for 78 minutes during a televised game in 2012 -- and raise inevitable questions about cardiovascular evaluation in endurance sports. In Italy, for example, the risk of sudden cardiac death is now considered so real that preparticipation screening (with ECG) is obligatory in all athletes and sports players.
This study's principal investigator Professor Friedrich Köhler confirmed that the risk of sudden cardiac death in endurance running is indeed "low," citing a 2012 study in which the incidence of cardiac arrests was put at 0.54 per 100,000 runners. However, he added that preparticipation screening is not able to detect this risk with any certainty.

Now, for real time evaluation to step up from proof of concept to the practical level, there are still technical problems to solve. "First," said Professor Köhler, "we need a way to handle the monitoring of, say, a thousand runners. One solution could be some 'intelligent' IT middleware, which might identify and select all pathological ECG findings for further analysis in the telemedical centre. And second, if the system does signal an abnormal ECG, how do we identify that individual runner at risk among so many runners -- and how do we alert the paramedics out on the course?"

Nevertheless, the two experiments reported today suggest that the concept works, and Professor Köhler indicated its high public health potential in other areas. "The marathon might be just a first indication for the continuous surveillance of vital parameters with mobile phone technology," he said. "There are opportunities in other endurance sports and even in other fields -- perhaps in the drivers of high speed express trains."

---

Story Source:

The above story is based on materials provided by European Society of Cardiology.Note: Materials may be edited for content and length.

---

Journal Reference:

1. S. Spethmann, S. Prescher, H. Dreger, H. Nettlau, G. Baumann, F. Knebel, F. Koehler. Electrocardiographic monitoring during marathon running: a proof of feasibility for a new telemedical approach. European Journal of Preventive Cardiology, 2014; 21 (2 Suppl): 32 DOI: 10.1177/2047487314553736

Two Papers are Ranked the No.1 and No.2 Most Cited Articles published in 2013 and 2014 in IEEE T-BME

Just know that my two papers are ranked the No.1 and No.2 Most Cited Articles Published in 2013 and 2014 in the journal IEEE Transactions on Biomedical Engineering. The journal link is here: http://tbme.embs.org/research-highlights/most-cited-articles/

The two papers are:

Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG via Block Sparse Bayesian Learning
Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao
IEEE Trans. on Biomedical Engineering, vol. 60, no. 2, pp. 300-309, 2013

[Remark: This paper used BSBL to reconstruct raw fetal ECG. It showed that BSBL can directly recover non-sparse correlated signals without using any dictionary matrix. It may be the first solid evidence showing that exploiting correlation is an effective way to reconstruct non-sparse signals in any domains.]

Compressed Sensing of EEG for Wireless Telemonitoring with Low Energy Consumption and Inexpensive Hardware
Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao
IEEE Trans. on Biomedical Engineering, vol. 60, no. 1, pp. 221-224, 2013[This paper applied BSBL to wireless telemonitoring of EEG, showing DCT coefficients can be recovered using block-structure model. Some explanations on why DCT dictionary matrix is effective for raw EEG are further given in my ST-SBL paper.]

What the Internet of Things Will Look Like in 2025 (Infographic)

There is a post in inc.com, showing the technical development and future of smart-home. It's very interesting and closely related to my research:

 http://www.inc.com/graham-winfrey/what-the-internet-of-things-will-look-like-in-2025.html?utm_content=buffer6d5c3

(Picture from the post in inc.com)

Use Block Sparse Bayesian Learning (BSBL) for Practical Problems

In LinkedIn, Phil, Leslie, and me have a productive discussion on the use of BSBL and EM-GM-AMP in practical problems. The whole discussions can be seen at here. For convenience, I copied my words on the use of BSBL and related issues below.

Below are several practical examples where intra-block correlation exists and BSBL can be used. In fact, there are many examples in practice.

1. Localization of distributed sources (not point-sources). In EEG/MEG source localization, the sources are generally not just a point. They have areas, so they are called distributed sources. When modeling the problem using a sparse linear regression model: y=Ax + v, the coefficient vector x is expected to contain several nonzero blocks, each nonzero block corresponding to a distributed source. Entries in the same nonzero block are highly correlated to each other in amplitude, since they are all associated with the same source.

(Remark: There are a number of work assuming the sources are point-sources as well. Thus the problem becomes a traditional DOA problem. However, in this case, BSBL can be applied as well, which I will explain later.)


2. In compressed sensing of ECG, an ECG signal has clear block structure (generally all the blocks are nonzero, but some blocks are very close to zero), and in each “block” the entries are highly correlated in amplitude. One can see the Fig.1 in my T-BME paper ( http://dsp.ucsd.edu/~zhilin/papers/Zhang_TBME2012.pdf ) to get such feeling.

(Remark: Almost all the physiological signals have correlation in the time domain, although some of them have not clear block-structure. However, BSBL can also be used for such signals. I will explain later).


3. One should note that the mathematical model used in compressed sensing is a linear regression model, and such a model has numerous applications in almost every field. For many applications, the regression coefficients have block structure. In each block, the entries are associated with a same physical “force” or a “factor”, and thus correlated in their amplitude.


In fact, as long as a signal has block structure, then it is highly possible that intra-block correlation also exists. Even if the intra-block correlation= 0, it is not harmful to run BSBL, because, as you can see from my T-SP paper, it also has excellent performance (and outperforms all the known block-structure-based algorithms) when intra-block correlation = 0. You do not need to test whether the correlation exists. You just need to run. That’s it. 


 Now I want to emphasize that BSBL can be used in the general-sparse problems (i.e., no structure in the coefficient vector x). This is due to two factors.

1.One factor is that truly sparse signals do not exist in most practical problems; in fact, they are non-sparse.

As I have mentioned in our personal communication, and also mentioned by Phil and many other people, the truly sparse signal does not exist in most practical problems. Those “sparse” signals are compressive; most of their entries in the time domain (or the coefficients in some transformed domains) are close to zero but strictly nonzero. In other words, they are non-sparse ! Using general-sparse recovery algorithms (such as Lasso, CoSaMP, OMP, FOCUSS, the basic SBL) can recover those entries with large amplitude. But they always have challenges in recovery of the entries with small amplitude. So, the quality of the recovered data has a “glass ceilling”, which is not very high.

However, BSBL has a unique property, i.e., recovering non-sparse signals (or signals with non-sparse representation coefficients) very well. As for the recovery of non-sparse signals, I do have a number of work showing this. Please refer to my T-BME papers:
[1] Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG via Block Sparse Bayesian Learning
[2] Compressed Sensing of EEG for Wireless Telemonitoring with Low Energy Consumption and Inexpensive Hardware

In fact, we have achieved much better results than [1-2], which will be release soon.


2.The second factor is that BSBL is a kind of multiscale regression algorithms (although very naïve).

In DOA or similar applications (e.g. earth-quake detection, brain source localization, or some communication problems), the matrix A (remind the model: y=Ax + v) is highly coherent (i.e., columns of A are highly correlated to each other). In this case, even if x is a very sparse vector, this problem is very difficult, especially in noisy situations. Using the basic SBL can get better performance than most existing algorithms. But we found that using BSBL can get much better performance. This is mainly because that BSBL, using the block partition, divides the whole search space (i.e. the number of whole locations in x) into a number of sub search spaces (i.e. the number of candidate nonzero blocks). This makes the localization problems become easier. Since x is sparse, generally the nonzero blocks are only a few and zero blocks are many. During iteration, the zero blocks are deleted in BSBL gradually. And the problem becomes easier and easier with iteration. I can dynamically change the block partition in BSBL according to some criterion. However, experience showed that it is not necessary to do this. BSBL can eventually find the correct locations of nonzero entries in x (although the rest entries in a nonzero block have very small amplitude).

The Fig.4 in my ICASSP 2012 paper ( http://sccn.ucsd.edu/~zhang/Zhang_ICASSP2012.pdf ) may give some feeling on what I said “the rest entries in a nonzero block have very small amplitude”.


Last, but not least, I want to say that a comparison between BSBL with other algorithms is helpful to everybody. I will be very happy to see the result. But I suggest one performs the comparison in some practical problems, since the readers generally come from various application fields with questions similar like “which algorithms is the best one for my problems”. Putting the comparison in specific practical problems is more informative and really helpful. Computer simulations have several problems, such as the suitable performance index, the consistency of the simulation model with the underlying models in practical problems, what’s the criterion to choose the algorithms (e.g. for an audio compressed sensing problem, does one think it is a general-sparse recovery problem, or a block-sparse recovery problem, or a non-sparse recovery problem?). Due to these issues, the conclusions may be not solid, and even more or less misleading.

MSE is generally not a good performance index. For example, for image quality, MSE is not recommended (what’s the suitable performance index for images is still a hot topic in the image processing field). In my experience on compressed sensing of EEG, I even found that MSE always misleading when I compared BSBL with my STSBL algorithms. This is why in my two T-BME papers (and other papers coming out), I used a task-oriented performance measure criterion. That is, after recovered the data,

(1) performing task-required signal processing or pattern recognition on the recovered data, obtaining result A;
(2) performing the same task-required signal processing or pattern recognition on the original data (or the recovered data by another algorithm), obtaining result B;
(3) comparing result A with result B, which tell me which algorithm has better data recovery ability. 


PS:
Many people asked me whether my BSBL codes can be used for complex-valued problems. My answer is YES. But you need to transform your complex-valued problem into a real-valued problem, as I showed here: https://sites.google.com/site/researchbyzhang/publication3/BSBL4complex.pdf?attredirects=0
This transform is very simple. You just need no more than 1 minute to do this.

I will update my BSBL codes in the near future such that no need to do the transform.

Compressed Sensing of EEG Using Wavelet Dictionary Matrices

Since my paper "Compressed Sensing of EEG for Wireless Telemonitoring with Low Energy Consumption and Inexpensive Hardware (IEEE T-BME, vol.60, no.1, 2013)" has been published, lots of people asked me how to do the compressed sensing of EEG using wavelets. Their problem was that Matlab has no function to generate the DWT basis matrix (i.e. the matrix D in my paper). One has to generate such matrices using other wavelet toolboxes. Now I updated my codes, where I gave a guide to generate such dictionary matrices using the wavelab (http://www-stat.stanford.edu/~wavelab/) , and there is a demo to show how to use a DWT basis matrix as the dictionary matrix for compressed sensing of EEG (demo_useDWT.m). The codes ('Compressed Sensing of EEG_v2.zip) can be downloaded at here

BTW: Please keep in mind that EEG is generally not sparse except to some special situations.

I successfully defended my Ph.D. dissertation today

I have two good reasons to remember today. One is that I successfully defended my Ph.D. dissertation today. The second is that today is 12/12/12 -- you won't have a day with this triple pattern again in this century :)

 (The EBU-1 building of UCSD; the little house on the top is the `falling star')

Welcome to attend my dissertation defense on Dec.12

Finally, my dissertation defense is scheduled at 9:15am - 11:15am on Dec.12 (Wednesday) in EBU1 4309.

Welcome to attend!

Below is the title and the abstract of my presentation.

Sparse Signal Recovery Exploiting Spatiotemporal Correlation

Sparse signal recovery algorithms have significant impact on many fields, including signal and image processing, information theory, statistics, data sampling and compression, and neuroimaging. The core of sparse signal recovery algorithms is to find a solution to an underdetermined inverse system of equations, where the solution is expected to be sparse or approximately sparse. Motivated by practical problems, numerous algorithms have been proposed. However, most algorithms ignore the correlation among nonzero entries of a solution, which is often encountered in a practical problem. Thus, it is unclear how this correlation affects an algorithm's performance and whether the correlation is harmful or beneficial.

This work aims to design algorithms which can exploit a variety of correlation structures in solutions and reveal the impact of these correlation structures on algorithms' recovery performance.

To achieve this, a block sparse Bayesian learning (BSBL) framework is proposed. Based on this framework, a number of sparse Bayesian learning (SBL) algorithms are derived to exploit intra-block correlation in a canonical block sparse model, temporal correlation in a canonical multiple measurement vector model, spatiotemporal correlation in a spatiotemporal sparse model, and local temporal correlation in a canonical time-varying sparse model. Several optimization approaches are employed in the algorithm development, including the expectation-maximization method, the bound-optimization method, and the fixed-point method. Experimental results show that these algorithms significantly outperform existing algorithms.

With these algorithms, we find that different correlation structures affect the quality of estimated solutions to different degrees. However, if these correlation structures are present and exploited, algorithms' performance can be largely improved. Inspired by this, we connect these algorithms to Group-Lasso type algorithms and iterative reweighted $\ell_1$ and $\ell_2$ algorithms, and suggest strategies to modify them to exploit the correlation structures for better performance.

The derived SBL algorithms have been used with considerable success in various challenging applications such as wireless telemonitoring of raw physiological signals and prediction of cognition levels of patients from their neuroimaging measures. In the former application, the derived SBL algorithms are the only algorithms so far that achieve satisfactory results. This is because raw physiological signals are neither sparse in the time domain nor sparse in any transformed domains, while the derived SBL algorithms can maintain robust performance for these signals. In the latter application, the derived SBL algorithms achieved the highest prediction accuracy on common datasets, compared to published results. This is because the BSBL framework provides flexibility to exploit both correlation structures and nonlinear relationship between response variables and predictor variables in regression models.

An new BSBL algorithm has been derived

A fast BSBL algorithm has been derived, and the work has been submitted to IEEE Signal Processing Letters.

Below is the paper:

Fast Marginalized Block SBL Algorithm
by Benyuan Liu, Zhilin Zhang, Hongqi Fan, Zaiqi Lu, Qiang Fu

The preprint can be downloaded at: http://arxiv.org/abs/1211.4909

Here is the abstract:
The performance of sparse signal recovery can be improved if both sparsity and correlation structure of signals can be exploited. One typical correlation structure is intra-block correlation in block sparse signals. To exploit this structure, a framework, called block sparse Bayesian learning (BSBL) framework, has been proposed recently. Algorithms derived from this framework showed promising performance but their speed is not very fast, which limits their applications. This work derives an efficient algorithm from this framework, using a  marginalized likelihood maximization method. Thus it can exploit block sparsity and intra-block correlation of signals. Compared to existing BSBL algorithms, it has close recovery performance to them, but has much faster speed. Therefore, it is more suitable for recovering large scale datasets.

Scientists See Promise in Deep-Learning Programs

The New York Times just has a report on  deep-learning. Some of the applications mentioned in the report  really refreshed my knowledge on it. Enjoy!

http://www.nytimes.com/2012/11/24/science/scientists-see-advances-in-deep-learning-a-part-of-artificial-intelligence.html?_r=0

Block Sparse Bayesian Learning (BSBL) has been accepted by IEEE Trans. on Signal Processing

Our work on Block Sparse Bayesian Learning (BSBL) has been accepted by IEEE Trans. on Signal Processing last week.

Here is the paper information:

Zhilin Zhang, Bhaskar. D. Rao, Extension of SBL Algorithms for theRecovery of Block Sparse Signals with Intra-Block Correlation, to appear in IEEE Trans. on Signal Processing

The preprint can be downloaded at: http://arxiv.org/abs/1201.0862
The codes can be downloaded at: https://sites.google.com/site/researchbyzhang/bsbl

Here is the abstract:

We examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting signals' intra-block correlation and the other by generalizing signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One family, directly derived from the BSBL framework, requires to know the block structure. Another family, derived from an expanded BSBL framework, is based on a weaker assumption on the block structure, and can be used in the case when the block structure is completely unknown. Using these algorithms we show that exploiting intra-block correlation is very helpful in improving recovery performance. These algorithms also shed light on how to modify existing algorithms or design new ones to exploit such correlation to improve performance.

The following are related application work:

Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Non-Invasive Fetal ECG via Block Sparse Bayesian Learning, IEEE Trans. Biomedical Engineering, 2012, accepted

Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, Compressed Sensing of EEG for Wireless Telemonitoring with Low Energy Consumption and Inexpensive Hardware, IEEE Trans. Biomedical Engineering, vol.59, no.12, 2012 



 

Our work on compressed sensing of fetal ECG has been accepted by IEEE T-BME

Our work on compressed sensing of fetal ECG has been accepted by IEEE Trans. Biomedical Engineering. The details are as follows:

Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Non-Invasive Fetal ECG via Block Sparse Bayesian Learning,  
by Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, accepted by IEEE Trans. Biomedical Engineering.   
Available at:  http://arxiv.org/abs/1205.1287, Codes can be downloaded at: http://dsp.ucsd.edu/~zhilin/BSBL.html, or  https://sites.google.com/site/researchbyzhang/bsbl


Note that there are two groups of works on compressed sensing of ECG. One is the ECG compression (just like video compression, image compression, etc). Most works actually belong to this group. They generally use some MIT-BIH datasets, which are very clean (noise is removed).

Another group is compressed sensing of ECG for energy-efficient wireless telemonitoring. There are only few works in this group. Our work belongs to this group. In this group the ECG data is always contaminated by noise and artifacts ('signal noise'). This is because the goal of telemonitoring is to allow people to walk and even exercise freely, and thus strong noise and artifacts caused by muscle and electrode movement are inevitable. Furthermore, artifacts caused by battery power level also cannot be ignored. Consequently, the raw ECG recordings are not sparse in the time domain and also not sparse in the transformed domains (e.g. the wavelet domain, the DCT domain). However, the strict constraint on energy consumption (and design issues, etc) of telemonitoring systems does not encourage filtering or other preprocessing before compression. Or, put in another way, if energy consumption and design issues are not problems, CS may have no advantages over traditional methods. Thus, CS algorithms have to recover non-sparse signals for this application. It turns out that the problem is very challenging.

Our work not only solves this challenging problem, but also has some interesting mathematical meanings:

By linear algebra, there are infinite solutions to the underdetermined problem y=Ax. When the true solution x0 is sparse, using CS algorithms it is possible to find it. But when the true solution x0 is non-sparse, finding it is more challenging and new constraints/assumptions are called for. This work shows that when exploiting the unknown block structure and the intra-block correlation of x0, it is possible to find a solution x_est which is very close to the true solution x0. These findings raise new and interesting possibilities for signal compression as well as theoretical questions in the subject of sparse and non-sparse signal recovery from a small number of measurements y.

Below is the paper's Abstract:
Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body-area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as non-sparsity and strong noise contamination, current CS algorithms generally fail in this application.

This work proposes to use the block sparse Bayesian learning (BSBL) framework to compress/reconstruct non-sparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.


PS: When I wrote this paper, I was in my wife's delivery room. My wife was lying on the bed, resting and waiting for her midwife. I was sitting beside her, writing the paper in my laptop (and trying to finish the main framework before the miracle moment). Now the baby is 8-month.

Yes, let's Move From Sparsity to Structured Sparsity

Igor wrote a cool post in Nuit Blanche yesterday: Pushing the Boundaries in Compressive Sensing by proposing the following questions (quoted below):

• Given that compressive sensing is based on an argument of sparsity 
• Given that sparsity is all around us because most data seem to be sparse or compressible in a wavelet basis
• Given that wavelet decomposition not only shows not just simple compressibility but structured compressibility of most datasets
• Given that we now have some results showing better compressive sensing with a structured sparsity argument

Isn't it time we stopped talking about RIP ? the Donoho-Tanner phase transition ? L_1 recovery ?

My answer is "YES"! There are a lot of practical scenarios where signals (or the regression coefficients) have rich structure. Merely exploiting sparsity without exploiting structure is far from enough! Even in some cases where structure information is not obvious and generally traditional L1 recovery algorithms are used, we can still find a way to use structured-sparsity-based algorithms.

In the following I'll give an example on the recovery of compressed audio signals, which is a typical application. I've seen a number of work which used traditional L1 algorithms to do the job. Let's see how a block-structure-exploited algorithm can improve the result.

Below is an audio signal with the length of 81920. 

In the compression stage, it was evenly divided into T segments x_i (i=1,2,...,T). We considered five cases, i.e., T choosing 160, 80, 40, 20, and 10. Accordingly, the segments had the length of N = 512, 1024, 2048, 4096, and 8192.  Each segment, x_i, was compressed into y_i. The sensing matrix A was a random Gaussian matrix with the dimension N/2 by N.

In the recovery stage, we first recovered the DCT coefficients of each segment, and then recovered the original segment. This is a tradition method used by most L1 algorithms for this task, since audio signals are believed to be more sparse than in the time domain.

We used six algorithms which do not consider any structure information. They were: Smooth L0 (SL0), EM-BG-AMP, SPGL-1, BCS, OMP, and SP. Their recovery performance was measured by total speed and the normalized MSE (calculated in dB). The results are given in the following table:

Table: Performance of all algorithms measured in terms of normalized MSE in dB (and speed in second).

From the Table, we can see if we want to obtain good quality, we need to increase the segment length. However, the cost is that the recovery time is significantly increased. For example, to achieve the quality of MSE = -21dB, SL0 needed to recover segments of the length 8192, and the total time was 2725 seconds!

Now let's perform the BSBL-BO algorithm, a sparse Bayesian learning algorithm exploiting block structure and intra-block correlation,  to do the same task. As I have said in many places, BSBL-BO needs users to define a block partition, and the block partition is not needed to be consistent with the true block structure of signals. So, we defined the block partition as (in Matlab language): [1:16:N]. The complete command for recovering the i-th segment was:

Result = BSBL_BO(A,  y_i, [1:16:N], 0, 'prune_gamma',-1, 'max_iters',15);

The recovery result for the case N=512 is given in the above Table. Clearly, by exploiting the structure information, BSBL-BO achieved -23.3 dB but only cost 82 seconds! The quality was 2 dB higher than that of SL0 but cost only 3% of the time cost by SL0.

What this result tells us? 

First, exploiting both structure and sparsity is very important; merely exploiting sparsity is outdated in many practical applications.

Second, conclusions on which algorithms are fast or slow are weakened if not mentioning which practical task is finished by these algorithms. Based on specific tasks, the answer could be varied case by case. For example, in the above experiment SL0 was very faster than BSBL-BO given the same segment length N. However, if the goal is to achieve a good quality, it took much longer time than BSBL-BO (even could not achieve the same quality as BSBL-BO, no matter how large the N was).

Note, I was not trying to compare BSBL-BO with the other algorithms. The comparison was not meaningful, since BSBL-BO exploits structure while the other algorithms do not. The point here is, even for some traditional applications where L1 algorithms were often used, exploiting structure information can provide you a better result!

PS: Recently we have an invited short review paper on SBL algorithms exploiting intra- and inter-vector correlation,
Bhaskar D. Rao, Zhilin Zhang, Yuzhe Jin, Sparse Signal Recovery in the Presence of Intra-Vector and Inter-Vector Correlation, SPCOM 2012
which can be accessed at: http://arxiv.org/pdf/1205.4471v1

Besides, several months ago we have another review paper on SBL algorithms exploiting structure, titled "From Sparsity to Structured Sparsity: Bayesian Perspective", in the Chinese journal Signal Processing. Those who can read Chinese can access the paper from here.

Our paper on compressed sensing of EEG has been accepted

Our paper on compressed sensing of EEG for wireless telemonitoring has been accepted by IEEE Trans. on Biomedical Engineering.

Here is the summary of this paper:
(1) EEG is not sparse in the time domain and not in transformed domains (e.g. the DCT domain, the wavelet domain).

(2) The BSBL framework is used to recover the non-sparse signals.

(3) The recovery quality is confirmed by independent component analysis decomposition, which is a regular processing procedure in EEG analysis.

(4) Neutral tone on the comparison of compressed sensing vs. wavelet compression is made.

This paper is our another paper on non-sparse signal recovery. It is also the first step of our big project on brain-computer interface (BCI). Although it is just accepted by the journal, the knowledge has been outdated for our lab, since I have a number of more powerful algorithm, which will be submitted soon.

Anyway, here is the paper:

Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, Compressed Sensing of EEG for Wireless Telemonitoring with Low Energy Consumption and Inexpensive Hardware, to appear in IEEE Trans. on Biomedical Engineering

Abstract:

Telemonitoring of electroencephalogram (EEG) through wireless body-area networks is an evolving direction in personalized medicine. Among various constraints in designing such a system, three important constraints are energy consumption, data compression, and device cost. Conventional data compression methodologies, although effective in data compression, consumes significant energy and cannot reduce device cost. Compressed sensing (CS), as an emerging data compression methodology, is promising in catering to these constraints. However, EEG is non-sparse in the time domain and also non-sparse in transformed domains (such as the wavelet domain). Therefore, it is extremely difficult for current CS algorithms to recover EEG with the quality that satisfies the requirements of clinical diagnosis and engineering applications. Recently, Block Sparse Bayesian Learning (BSBL) was proposed as a new method to the CS problem. This study introduces the technique to the telemonitoring of EEG. Experimental results show that its recovery quality is better than state-of-the-art CS algorithms, and sufficient for practical use. These results suggest that BSBL is very promising for telemonitoring of EEG and other non-sparse physiological signals.

The code and related data can be downloaded at: https://sites.google.com/site/researchbyzhang/bsbl, or http://dsp.ucsd.edu/~zhilin/BSBL.html