Lensless single pixel cameras are pretty cool… let’s simulate one!

So, a while back I stumbled across this article: http://www.technologyreview.com/view/515651/bell-labs-invents-lensless-camera/

To summarize it, Bell Labs built a single pixel camera that needs no lenses to operate… pretty cool concept right? I immediately wanted to build one.

After doing some research, I realized the concept was pretty simple: place an array of selectively-blackable windows in front of a light sensor like a photodiode, send random patterns to the windows, record the light level at the photodiode, repeat a few thousand times, and all of a sudden you’re left with a giant system of linear equations, the solution to which is the image the camera “sees”.

The problem arises when you try to solve this system. The system is HUGE, so there’s no way you could solve it through gaussian elimination, so instead we solve the system through minimizing the system’s l1 norm, and a least-squares method.

As I’m in Princeton for my summer job at PPPL, I’m lacking my workshop and tools, so I couldn’t actually build a single pixel camera. Instead I did the next best thing. I programmed a simulation of one in Matlab.

I used this awesome l1-minimization system solving library called l1_ls from Stanford, and after writing some Matlab code, I was able to “take a picture” of a  256×256 pixel image.
Below is the reconstructed image, taken from 10,000 “exposures” of the virtual single pixel camera, followed by the original image.

It’s not much, but it’s something. It’s a start.

The next step on the-programming side is to use Hadamard matricies rather than pseudorandom matricies to generate the sampling patterns. Other groups have done this, and I’m hoping it will help “distribute the sparsity” of the sampling matricies, resulting in a better final image. The step after this is to build one… and maybe one that works in the IR, UV, microwave, or x-ray spectrum.

ImageImage

Next step: building one.

About these ads

20 thoughts on “Lensless single pixel cameras are pretty cool… let’s simulate one!

  1. I’ll immediately grasp your rss feed as I can not to find
    your e-mail subscription hyperlink or newsletter service.
    Do you have any? Please allow me recognize
    so that I may subscribe. Thanks.

  2. What i don’t understood is in reality how you’re not really much
    more neatly-preferred han you might be now. You’re very intelligent.
    You already know therefore considerably relating to
    this matter, produced me individually consider it
    from a lot of numerous angles. Its like women and men aren’t involved until it’s
    one thing to accomplish with Girl gaga! Your individual stuffs
    outstanding. All the time deal with it up!

  3. You really make it appear really easy together with your presentation however I in finding this matter to be really one thing that I
    feel I might never understand. It kind of feels
    too complex and extremely vast for me. I’m having a look ahead for your next post, I will try
    to get the hang of it!

  4. I do not know if it’s just me or if perhaps everyone
    else experiencing problems with your blog. It looks like some of the written text in your content are running
    off the screen. Can someone else please comment and let me know
    if this is happening to them as well? This may be a problem with my
    internet browser because I’ve had this happen previously.
    Appreciate it

  5. Yet, living under the same roof, it becomes a little obvious to read the body language of your partner at some usual
    moments. In light of the ongoing research for, and
    by, the National Highway Traffic Safety Administration ( we should at least consider their policy on using
    cell phones while driving that states “The primary responsibility of the driver is to operate a motor vehicle safely. Not exactly the stablest premise, coming from the traditionalist camp: it’d be a huge upset, and mobile companies just aren’t comfortable with that.

  6. scholl express pedi woolworths

    Scholl Express Pedi hard skin remover leaves the skin feeling soft and smooth from the very first use.
    This unit is exclusively designed to empower the professional removal of
    hard pores and skin in the feet, appropriate in ease and
    comfort of your very own house.

    The epidermis around the feet was made to endure the daily strain of taking walks
    and standing upright. Sometimes constant pressure
    or rubbing from bad fitting boots and shoes might lead to
    hard skin to build. Foot care for healthy toes is significant; after all, they are with you for
    the lifetime.

    Wonderfully and anatomically manufactured, the Scholl Express Pedi unique
    roller surface area will make it effortless to successfully
    eradicate unattractive and often unpleasant really tough skin
    safely. Very small microgranuals inlayed in to the Scholl Express Pedi roller, very carefully buff away challenging skin, with no resorting to blades.

    To attain your personal professional-style home pedicure, just roll over the
    required area with medium to light pressure motions; just replicate regularly for sleek and
    gentle sensation toes. In addition, the Scholl Express Pedi is
    safeguarded by means of a two years warranty, and integrated are 2x AA batteries which means you could make a start removing useless skin cells quickly.

    For beautiful, silky-soft skin have a look at
    the Scholl Express Pedi to revitalise the feet. The revolving head will get rid of unwanted, dry skin from
    feet rapidly, due to mineral micro-grains embedded in the head of the product.
    The Scholl Express Pedi is completely risk-free to use.
    There are no sharp edges or blades and it will come total with a safety stop button.

    The Scholl Express Pedi is an all round professional skin treatment device.

    It’s so simple to use, brings about no discomfort and aids you receive the
    specified benefits of the perfect pedicure. For hygeine purposes, antimicrobial
    treatment gets rid of bacteria existing around the roller head.

  7. Hi there! This is my first comment here so I just wanted to give a
    quick shout out and say I really enjoy reading your blog posts.

    Can you suggest any other blogs/websites/forums that cover the
    same topics? Thanks for your time!

  8. Awesome blog! Do youu have any tips for aspiring writers?
    I’m planning to start my oown website soon bbut I’m a little lost on everything.
    Would yoou suggest starting with a free platfoprm like Worfdpress or go for
    a paid option? There are soo many choices out there
    that I’m totally overwhelmed .. Anyy tips? Kudos!

  9. These are normally rather small units which have been created
    to present feasible consuming h2o when you are not near a taken care of drinking water supply (untreated drinking water sources
    include lakes, rivers, streams, and many others.
    Cruise vacations make it possible to pay one price and spend days to a week relaxing by the poolside.
    Investing in your company’s retirement plan is one option but there
    are other options.

  10. Sweet blog! I found it while searching on Yahoo
    News. Do you have any tips on how to get listed in Yahoo News?
    I’ve been trying for a while but I never seem to get there!
    Thank you

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s