{"id":99,"date":"2023-12-17T14:05:38","date_gmt":"2023-12-17T19:05:38","guid":{"rendered":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/?page_id=99"},"modified":"2023-12-18T14:03:08","modified_gmt":"2023-12-18T19:03:08","slug":"fall-progress","status":"publish","type":"page","link":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/","title":{"rendered":"Progress (Fall 2023)"},"content":{"rendered":"\n

See Introduction<\/a> for a description of the background and rationale behind these updates.<\/p>\n\n\n\n

Poisson-Noise MLE<\/h2>\n\n\n\n

The classical phase-retrieval pipeline from Kotwal et al. 2022<\/a>, as described in the Introduction<\/a>, assumes a Gaussian noise model. While this is an appropriate model for read (sensor) noise<\/a>, which is related to a camera’s circuitry and sensitivity, we can expect noise in the SWI frame capture process to be dominated by shot noise<\/a>, which follows a Poisson distribution.<\/p>\n\n\n\n

Changing the classical reconstruction pipeline to implement an MLE based on a Poisson noise model improves the output reconstruction by some 10%. Note the clearer boundaries and flatter surfaces in the Poisson reconstruction on the right.<\/p>\n\n\n\n

\n
\"\"
(a)<\/figcaption><\/figure>\n\n\n\n
\"\"
(b)<\/figcaption><\/figure>\n\n\n\n
\"\"
(c)<\/figcaption><\/figure>\n
Figure 9. (a)<\/strong> Reconstruction from OCT. (b)<\/strong> Reconstruction from SWI with bilateral filter and Gaussian MLE. (c)<\/strong> Reconstruction from SWI with bilateral filter and Poisson MLE.<\/figcaption><\/figure>\n\n\n\n

Self-Supervised Image Formation MLP<\/h2>\n\n\n\n

Eventually, our goal is to demonstrate a neural network that incorporates the results of this project into a learned phase-recovery function that performs better than the classical pipeline. We know that this network will contain the differentiable bilateral solver<\/a> as a module, but the rest of the architecture is still being designed.<\/p>\n\n\n\n

A simple approach is to implement phase retrieval as a pixelwise MLP. This MLP should be able to learn different representations of the underlying data. One particularly useful representation to learn is a four-parameter image formation model<\/strong>, which can then be used to reconstruct the sixteen intensity images we started with.<\/p>\n\n\n\n

This is a useful representation for two reasons:<\/p>\n\n\n\n

    \n
  1. The fact that we can fully reconstruct the intensity images means that we can train the network in a self-supervised fashion. Since the intensity images are the input and the image formation parameters are the output, the reconstructed intensity images lend themselves to a natural reconstruction loss function with no need for ground-truth labels.<\/li>\n\n\n\n
  2. One of the output image formation parameters is the phase, which is more or less the goal of the pipeline (since the phase difference is proportional to depth).<\/li>\n<\/ol>\n\n\n\n

    In particular, the four image formation parameters, denoted A<\/em>, B<\/em>, a<\/em>, and f<\/em>, satisfy the following relationship to the intensity I<\/em> for each of i<\/em> \u2208 {0, 1, 2, 3} and j<\/em> \u2208 {0, 1, 2, 3} (that is, the grid of M<\/em> times N<\/em> shifts according to the method used<\/a> to capture the intensity images):<\/p>\n\n\n

    \n
    \"\"<\/figure>\n<\/div>\n\n\n

    Note that in this model, A<\/em>, B<\/em>, a<\/em>, and of course I<\/em> vary according to pixel location u,v<\/em>, while f<\/em> does not. Accordingly, the neural network is trained to learn<\/em> an explicit parameter f<\/em> and output<\/em> A<\/em>, B<\/em>, and a<\/em>.<\/p>\n\n\n

    \n
    \"\"
    Figure 10. Output image formation parameters given intensity frames below. Note that f<\/em> is defined to be static across the entire image.<\/figcaption><\/figure>\n<\/div>\n\n\n
    \n
    \"\"
    (a)<\/figcaption><\/figure>\n\n\n\n
    \"\"
    (b)<\/figcaption><\/figure>\n
    Figure 11. (a)<\/strong> Original intensity images. (b)<\/strong> Reconstructed intensity frames.<\/figcaption><\/figure>\n\n\n\n

    Confidence measure using error propagation<\/h2>\n\n\n
    \n
    \"\"
    Figure 12.<\/em> Confidence metric used in Fast Bilateral Solver. Note the higher confidence values in flat regions of the coin compared to areas around the grooves of the coin.<\/figcaption><\/figure>\n<\/div>\n\n\n

    We represent the confidence of our initial phase estimate using error propagation on the first-order Taylor approximation of f<\/em><\/strong>, the phase estimation function (in our case MLE). First we take the Taylor approximation:<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    using the formula for error propagation (or variance propagation), we retrieve the estimated variance of the output of our estimation function:<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n
    \"\"<\/figure>\n\n\n\n

    We take the inverse of the variance as our confidence metric by calculating a<\/strong><\/em> using autodiff libraries:<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    This method can be generalized to any neural network by setting f<\/strong><\/em> as the network, as long as we can use autodiff to approximate the first-order derivative of the output with regards to the input. Providing the confidence image as input to the Fast Bilateral Solver resulted in a 70% error reduction<\/strong> in the final depth estimation compared to using the Fast Bilateral Solver with a constant confidence value, which would be equivalent to applying a bilateral filter.<\/p>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    See Introduction for a description of the background and rationale behind these updates. Poisson-Noise MLE The classical phase-retrieval pipeline from Kotwal et al. 2022, as described in the Introduction, assumes a Gaussian noise model. While this is an appropriate model for read (sensor) noise, which is related to a camera’s circuitry and sensitivity, we can … <\/p>\n

    Continue reading “Progress (Fall 2023)”<\/span><\/a><\/p>\n","protected":false},"author":176,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-99","page","type-page","status-publish","hentry"],"yoast_head":"\nProgress (Fall 2023) - Neural Synthetic Wavelength Interferometry<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Progress (Fall 2023) - Neural Synthetic Wavelength Interferometry\" \/>\n<meta property=\"og:description\" content=\"See Introduction for a description of the background and rationale behind these updates. Poisson-Noise MLE The classical phase-retrieval pipeline from Kotwal et al. 2022, as described in the Introduction, assumes a Gaussian noise model. While this is an appropriate model for read (sensor) noise, which is related to a camera’s circuitry and sensitivity, we can … Continue reading "Progress (Fall 2023)"\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/\" \/>\n<meta property=\"og:site_name\" content=\"Neural Synthetic Wavelength Interferometry\" \/>\n<meta property=\"article:modified_time\" content=\"2023-12-18T19:03:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-content\/uploads\/sites\/89\/2023\/12\/soap_oct.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/\",\"url\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/\",\"name\":\"Progress (Fall 2023) - Neural Synthetic Wavelength Interferometry\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/wp-content\\\/uploads\\\/sites\\\/89\\\/2023\\\/12\\\/soap_oct.png\",\"datePublished\":\"2023-12-17T19:05:38+00:00\",\"dateModified\":\"2023-12-18T19:03:08+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/#primaryimage\",\"url\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/wp-content\\\/uploads\\\/sites\\\/89\\\/2023\\\/12\\\/soap_oct.png\",\"contentUrl\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/wp-content\\\/uploads\\\/sites\\\/89\\\/2023\\\/12\\\/soap_oct.png\",\"width\":400,\"height\":578},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/fall-progress\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Progress (Fall 2023)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/#website\",\"url\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/\",\"name\":\"Neural Synthetic Wavelength Interferometry\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/mscvprojects.ri.cmu.edu\\\/f23team12\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Progress (Fall 2023) - Neural Synthetic Wavelength Interferometry","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/","og_locale":"en_US","og_type":"article","og_title":"Progress (Fall 2023) - Neural Synthetic Wavelength Interferometry","og_description":"See Introduction for a description of the background and rationale behind these updates. Poisson-Noise MLE The classical phase-retrieval pipeline from Kotwal et al. 2022, as described in the Introduction, assumes a Gaussian noise model. While this is an appropriate model for read (sensor) noise, which is related to a camera’s circuitry and sensitivity, we can … Continue reading \"Progress (Fall 2023)\"","og_url":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/","og_site_name":"Neural Synthetic Wavelength Interferometry","article_modified_time":"2023-12-18T19:03:08+00:00","og_image":[{"url":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-content\/uploads\/sites\/89\/2023\/12\/soap_oct.png","type":"","width":"","height":""}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"6 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/","url":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/","name":"Progress (Fall 2023) - Neural Synthetic Wavelength Interferometry","isPartOf":{"@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/#primaryimage"},"image":{"@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/#primaryimage"},"thumbnailUrl":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-content\/uploads\/sites\/89\/2023\/12\/soap_oct.png","datePublished":"2023-12-17T19:05:38+00:00","dateModified":"2023-12-18T19:03:08+00:00","breadcrumb":{"@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/#primaryimage","url":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-content\/uploads\/sites\/89\/2023\/12\/soap_oct.png","contentUrl":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-content\/uploads\/sites\/89\/2023\/12\/soap_oct.png","width":400,"height":578},{"@type":"BreadcrumbList","@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/fall-progress\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/"},{"@type":"ListItem","position":2,"name":"Progress (Fall 2023)"}]},{"@type":"WebSite","@id":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/#website","url":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/","name":"Neural Synthetic Wavelength Interferometry","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/pages\/99","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/users\/176"}],"replies":[{"embeddable":true,"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/comments?post=99"}],"version-history":[{"count":15,"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/pages\/99\/revisions"}],"predecessor-version":[{"id":135,"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/pages\/99\/revisions\/135"}],"wp:attachment":[{"href":"https:\/\/mscvprojects.ri.cmu.edu\/f23team12\/wp-json\/wp\/v2\/media?parent=99"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}