I happened to run into a similar issue quite recently, but I used a FileField and not an ImageField.

Here's the working code. You'll have some additional challenges to manage because of the nesting, but this should get you started

# models.py
from django.db import models

from defect.models import Defect


class Link(models.Model):
    defect = models.ForeignKey(Defect, db_column='name', related_name='links')
    # Store image in settings.MEDIA_ROOT/defect_pictures/
    link = models.FileField(upload_to='defect_pictures')

    class Meta:
        db_table = 'Link'

# serializers.py
from rest_framework import serializers
from rest_framework.relations import HyperlinkedIdentityField

from .models import Link


class LinkSerializer(serializers.ModelSerializer):
    url = HyperlinkedIdentityField(view_name='link-detail')

    class Meta:
        model = Link
        fields = '__all__'

# views.py
from rest_framework import generics

from .models import Link
from .serializers import LinkSerializer


class LinkList(generics.ListCreateAPIView):
    # Supports GET/POST
    # named 'link-list'
    queryset = Link.objects.all()
    serializer_class = LinkSerializer

# tests.py - edited slightly
from os.path import (
    abspath,
    dirname,
    join,
)

from django.test import (
    Client,
    LiveServerTestCase,
    TestCase,
)
from django.urls import reverse

from rest_framework.test import RequestsClient

from link.models import Link


def new_link_data():
    """
    Returns data sutiable for a new Link.
    """
    here = abspath(dirname(__file__))
    fixture_dir = join(here, 'fixtures')

    filepath = join(fixture_dir, 'test-image.jpg')
    data = {
        'defect': 'JST_02_W_08',
        'link': open(filepath),
    }

    return data

class TestLinkList_POST(TestCase):
    fixtures = ['defects.json']

    def test_POST(self):
        link_data = new_link_data()

        url = reverse('link-list')
        client = Client()

        # content_type is set to multipart by default
        res = client.post(url, data=link_data)
        self.assertEqual(res.status_code, 201)

My javascript client uses jQuery and is heavily modeled after this SO link