Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

any assistance would be appreciated in python data = https://drive.google.com/file/d/1P4wlaQZ-ISjxALi_Pohuc1e6Y-INbfRM/view?usp=sharing Medical imaging reconstruction. (10 points) In this problem, you will consider an example resembles medical

any assistance would be appreciated in python

data = https://drive.google.com/file/d/1P4wlaQZ-ISjxALi_Pohuc1e6Y-INbfRM/view?usp=sharing

image text in transcribed
Medical imaging reconstruction. (10 points) In this problem, you will consider an example resembles medical imaging reconstruction in MRI. We begin with a true image image of dimension 50 X 50 (i.e., there are 2500 pixels in total). Data is cs.mat; you can plot it rst. This image is truly sparse, in the sense that 2084 of its pixels have a value of 0, while 416 pixels have a value of 1. You can think of this image as a toy version of an MRI image that we are interested in collecting. Because of the nature of the machine that collects the MRI image, it takes a long time to measure each pixel value individually, but it's faster to measure a linear combination of pixel values. We measure it = 1300 linear combinations, with the weights in the linear combination being random, in fact, independently distributed as N(0, 1). Because the machine is not perfect, we don't get to observe this directly, but we observe a noisy version. These measurements are given by the entries of the vector y:A:c+n, where y E R1300, A E RIBDOXQWO, and n N N(0, 25 X Ilgoo) where L, denotes the identity matrix of size n X n. In this homework, you can generate the data 3; using this model. Now the question is: can we model 3,; as a linear combination of the columns of a: to recover some coeicient vector that is close to the image? Roughly speaking, the answer is yes. Key points here: although the number of measurements it = 1300 is smaller than the dimension p : 2500, the true image is sparse. Thus we can recover the sparse image using few measurements exploiting its structure. This is the idea behind the eld of compressed sensing. The image recovery can be done using lasso mgnlly AxH Huxnl. (a) (5 points) Now use lasso to recover the image and select A using 10-fold cross-validation. Plot the cross~validation error curves, and show the recovered image

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Mathematical Analysis For Quantitative Finance

Authors: Daniele Ritelli, Giulia Spaletta

1st Edition

1351245104, 9781351245104

More Books

Students also viewed these Mathematics questions

Question

Distinguish between apperception and perception.

Answered: 1 week ago

Question

CPU meaning

Answered: 1 week ago