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Notes from the Frontiers of Mathematics

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Tag: compression

What Is Relative Entropy?

December 13, 2014 ~ Prateek Joshi ~ 2 Comments

In this blog post, we will be using a bit of background from my previous blog post. If you are familiar with the basics of entropy coding, you should be fine. If not, you may want to quickly read through my previous blog post. So coming to the topic at hand, let's continue our discussion … Continue reading What Is Relative Entropy?

What Is Entropy Coding?

December 6, 2014 ~ Prateek Joshi ~ 1 Comment

Entropy Coding appears everywhere in modern digital systems. It is a fundamental building block of data compression, and data compression is pretty much needed everywhere, especially for internet, video, audio, communication, etc. Let's consider the following scenario. You have a stream of English alphabets coming in and you want to store them in the best … Continue reading What Is Entropy Coding?

Reading JPEG Into A Byte Array

December 28, 2013December 29, 2013 ~ Prateek Joshi ~ Leave a comment

Let's say you are working with images for your project. A lot of times, when you have to work across multiple platforms, the encoding doesn't remain the same. In these scenarios, you cannot process images directly by treating them like 2D matrices. One of the most common image formats you will comes across is JPEG. … Continue reading Reading JPEG Into A Byte Array

Digital Watermarking

March 25, 2013November 1, 2013 ~ Prateek Joshi ~ 3 Comments

Let's say you want to verify the authenticity of a signal. The signal can take any form like an image, audio, video, or any other kind of bit stream. By now, everybody would have heard the term "watermark" being used in the general sense. The most common example would be currency notes. Watermarks are embedded … Continue reading Digital Watermarking

Image Steganography

March 20, 2013November 1, 2013 ~ Prateek Joshi ~ 3 Comments

As discussed in my previous post, steganography is the art of hiding the fact that communication is taking place. We achieve this by hiding original information inside other information known as carrier files. Many different carrier file formats can be used, but digital images are the most popular because of their frequency of occurrence on … Continue reading Image Steganography

The Ramifications Of H.265

January 28, 2013November 1, 2013 ~ Prateek Joshi ~ 1 Comment

The International Telecommunication Union (ITU) recently approved the next generation video format known as H.265, which would be the successor to the current H.264 standard. H.265, also informally known as High Efficiency Video Coding (HEVC), is supposed to be twice as efficient as H.264 in terms of compression. H.265 relies on the fact that processing … Continue reading The Ramifications Of H.265

Principal Component Analysis

September 21, 2012November 4, 2013 ~ Prateek Joshi ~ 1 Comment

Principal Component Analysis (PCA) is one of most useful tools in the field of pattern recognition. Let's say you are making a list of people and collecting information about their physical attributes. Some of the more common attributes include height, weight, chest, waist and biceps. If you store 5 attributes per person, it is equivalent … Continue reading Principal Component Analysis

Wavelet Analysis

September 13, 2012September 13, 2012 ~ Prateek Joshi ~ 3 Comments

Wavelets are actually a topic of pure mathematics. But over the last couple of decades, they have shown great promise and are now being adapted for a vast number of applications. They are used in image compression, molecular dynamics, seismology, physics, DNA analysis etc. One of the main advantages of wavelet analysis is the amount … Continue reading Wavelet Analysis

Fourier Analysis

September 5, 2012 ~ Prateek Joshi ~ 6 Comments

Most of the people in the tech field have already heard about Fourier analysis by now. Some of them love it, some of them hate it and the remaining few are just not sure what it is! Fourier analysis is one of the most fundamental tools in the field of engineering and technology. In fact, … Continue reading Fourier Analysis

Good Things Come In Small Packages

June 13, 2012October 17, 2015 ~ Prateek Joshi ~ 1 Comment

We encounter digital images everyday. We see a lot of JPEG files on our computers, cameras, phones and tablets. The actual images are huge and it should actually take up a lot of space to fit in all that data. But somehow our machines are able to compress all those images and store everything compactly. … Continue reading Good Things Come In Small Packages

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